| {{ KNOWL("modcurve.level", "Level") }}: | ${{ curve.level }}$ | {{ KNOWL("modcurve.sl2level", "$\SL_2$-level") }}: | ${{ curve.sl2level }}$ | {% if curve.genus > 0 %} | {{ KNOWL("modcurve.newform_level", "Newform level:") }} | ${{ curve.newform_level }}$ | {% endif %}|
| {{ KNOWL("modcurve.index", "Index") }}: | ${{ curve.index }}$ | {{ KNOWL("modcurve.psl2index", "$\PSL_2$-index") }}: | ${{ curve.psl2index }}$ | ||||
| {{ KNOWL("modcurve.genus", "Genus") }}: | ${{ curve.genus }} = 1 + \frac{ {{curve.psl2index}} }{12} - \frac{ {{curve.nu2}} }{4} - \frac{ {{curve.nu3}} }{3} - \frac{ {{curve.cusps}} }{2}$ | ||||||
| {{ KNOWL("modcurve.cusps", "Cusps") }}: | {{ curve.cusps_display }} | {{ KNOWL("modcurve.cusp_widths", "Cusp widths") }} | {{ curve.cusp_widths_display }} | {{ KNOWL("modcurve.cusp_orbits", "Cusp orbits") }} | {{ curve.cusp_orbits_display }} | ||
| {{ KNOWL("modcurve.elliptic_points", "Elliptic points") }}: | ${{curve.nu2}}$ of order $2$ and ${{curve.nu3}}$ of order $3$ | ||||||
| {{ KNOWL("modcurve.level", "Level") }}: | +${{ curve.level }}$ | + | {{ KNOWL("modcurve.sl2level", "$\SL_2$-level") }}: | +${{ curve.sl2level }}$ | + {% if curve.genus > 0 %} + | {{ KNOWL("modcurve.newform_level", "Newform level:") }} | +${{ curve.newform_level }}$ | + {% endif %}
| {{ KNOWL("modcurve.index", "Index") }}: | ${{ curve.index }}$ | + | {{ KNOWL("modcurve.psl2index", "$\PSL_2$-index") }}: | ${{ curve.psl2index }}$ | |||
| {{ KNOWL("modcurve.genus", "Genus") }}: | +${{ curve.genus }} = 1 + \frac{ {{curve.psl2index}} }{12} - \frac{ {{curve.nu2}} }{4} - \frac{ {{curve.nu3}} }{3} - \frac{ {{curve.cusps}} }{2}$ | +||||||
| {{ KNOWL("modcurve.cusps", "Cusps") }}: | +{{ curve.cusps_display }} | + | {{ KNOWL("modcurve.cusp_widths", "Cusp widths") }} | +{{ curve.cusp_widths_display }} | + | {{ KNOWL("modcurve.cusp_orbits", "Cusp orbits") }} | +{{ curve.cusp_orbits_display }} | +
| {{ KNOWL("modcurve.elliptic_points", "Elliptic points") }}: | +${{curve.nu2}}$ of order $2$ and ${{curve.nu3}}$ of order $3$ | +||||||
| {{ KNOWL('modcurve.rank', 'Analytic rank') }}: | {% if curve.rank is not none %} ${{ curve.rank }}$ {% else %} not computed {% endif %} | ||||||
| {{ KNOWL('modcurve.rank', 'Analytic rank') }}: | +{% if curve.rank is not none %} ${{ curve.rank }}$ {% else %} not computed {% endif %} | +||||||
| {{ KNOWL("modcurve.gonality", "$\Q$-gonality")}}: | ${{ curve.q_gonality if curve.q_gonality else "%s \\le \\gamma \\le %s"%(curve.q_gonality_bounds[0],curve.q_gonality_bounds[1]) }}$ | ||||||
| {{ KNOWL("modcurve.gonality", "$\overline{\Q}$-gonality")}}: | ${{ curve.qbar_gonality if curve.qbar_gonality else "%s \\le \\gamma \\le %s"%(curve.qbar_gonality_bounds[0],curve.qbar_gonality_bounds[1]) }}$ | ||||||
| {{ KNOWL("modcurve.cusps", "Rational cusps") }}: | ${{ curve.rational_cusps }}$ | ||||||
| {{ KNOWL("modcurve.cm_discriminants", "Rational CM points") }}: | {{ "yes $\quad(D =$ $%s$)"%(curve.cm_discriminant_list) if curve.cm_discriminants else "none" }} | ||||||
| {{ KNOWL("modcurve.gonality", "$\Q$-gonality")}}: | +${{ curve.q_gonality if curve.q_gonality else "%s \\le \\gamma \\le %s"%(curve.q_gonality_bounds[0],curve.q_gonality_bounds[1]) }}$ | +||||||
| {{ KNOWL("modcurve.gonality", "$\overline{\Q}$-gonality")}}: | +${{ curve.qbar_gonality if curve.qbar_gonality else "%s \\le \\gamma \\le %s"%(curve.qbar_gonality_bounds[0],curve.qbar_gonality_bounds[1]) }}$ | +||||||
| {{ KNOWL("modcurve.cusps", "Rational cusps") }}: | +${{ curve.rational_cusps }}$ | +||||||
| {{ KNOWL("modcurve.cm_discriminants", "Rational CM points") }}: | +{{ "yes $\quad(D =$ $%s$)"%(curve.cm_discriminant_list) if curve.cm_discriminants else "none" }} | +
| {{ KNOWL('modcurve.other_labels', 'Cummins and Pauli (CP) label') }}: | {{curve.CPlabel}} |
| {{ KNOWL('modcurve.other_labels', 'Sutherland and Zywina (SZ) label') }}: | {{curve.SZlabel}} |
| {{ KNOWL('modcurve.other_labels', 'Rouse and Zureick-Brown (RZB) label') }}: | {{curve.RZBlabel}} |
| {{ KNOWL('modcurve.other_labels', 'Rouse, Sutherland, and Zureick-Brown (RSZB) label') }}: | {{curve.RSZBlabel}} |
| {{ KNOWL('ec.galois_rep_modell_image', 'Sutherland (S) label') }}: | {{curve.Slabel}} |
| {{ KNOWL('modcurve.other_labels', 'Cummins and Pauli (CP) label') }}: | +{{curve.CPlabel}} | +
| {{ KNOWL('modcurve.other_labels', 'Sutherland and Zywina (SZ) label') }}: | +{{curve.SZlabel}} | +
| {{ KNOWL('modcurve.other_labels', 'Rouse and Zureick-Brown (RZB) label') }}: | +{{curve.RZBlabel}} | +
| {{ KNOWL('modcurve.other_labels', 'Rouse, Sutherland, and Zureick-Brown (RSZB) label') }}: | +{{curve.RSZBlabel}} | +
| {{ KNOWL('ec.galois_rep_modell_image', 'Sutherland (S) label') }}: | +{{curve.Slabel}} | +
| {{ KNOWL('modcurve.level_structure', '$\GL_2(\Z/%s\Z)$-generators'%(curve.level)) }}: | {{ curve.show_generators()}} |
| {{ KNOWL('modcurve.level_structure', '$\GL_2(\Z/%s\Z)$-subgroup'%(curve.level)) }}: | {{ curve.show_subgroup() | safe}} |
| {{ KNOWL('modcurve.contains_negative_one', 'Contains $-I$') }}: | {{ curve.coarse_description | safe }} |
| {{ KNOWL('modcurve.quadratic_refinements', 'Quadratic refinements') }}: | {{ curve.quadratic_refinements | safe }} |
| {{ KNOWL('modcurve.level_structure', 'Cyclic '+(curve.level|string)+'-isogeny field degree') }}: | ${{ curve.cyclic_isogeny_field_degree() }}$ |
| {{ KNOWL('modcurve.level_structure', 'Cyclic '+(curve.level|string)+'-torsion field degree') }}: | ${{ curve.cyclic_torsion_field_degree() }}$ |
| {{ KNOWL('modcurve.level_structure', 'Full '+(curve.level|string)+'-torsion field degree') }}: | ${{ curve.full_torsion_field_degree() }}$ |
| {{ KNOWL('modcurve.level_structure', '$\GL_2(\Z/%s\Z)$-generators'%(curve.level)) }}: | +{{ curve.show_generators()}} | +
| {{ KNOWL('modcurve.level_structure', '$\GL_2(\Z/%s\Z)$-subgroup'%(curve.level)) }}: | +{{ curve.show_subgroup() | safe}} | +
| {{ KNOWL('modcurve.contains_negative_one', 'Contains $-I$') }}: | +{{ curve.coarse_description | safe }} | +
| {{ KNOWL('modcurve.quadratic_refinements', 'Quadratic refinements') }}: | +{{ curve.quadratic_refinements | safe }} | +
| {{ KNOWL('modcurve.level_structure', 'Cyclic '+(curve.level|string)+'-isogeny field degree') }}: | +${{ curve.cyclic_isogeny_field_degree() }}$ | +
| {{ KNOWL('modcurve.level_structure', 'Cyclic '+(curve.level|string)+'-torsion field degree') }}: | +${{ curve.cyclic_torsion_field_degree() }}$ | +
| {{ KNOWL('modcurve.level_structure', 'Full '+(curve.level|string)+'-torsion field degree') }}: | +${{ curve.full_torsion_field_degree() }}$ | +
| {{ KNOWL('ag.conductor', 'Conductor') }}: | ${{ curve.factored_conductor }}$ |
| - {{ KNOWL('av.simple', 'Simple') }}: - | -- {% if curve.simple %} - yes - {% elif curve.simple is not none %} - no - {% else %} - not computed - {% endif %} - | -
| - {{ KNOWL('av.squarefree', 'Squarefree') }}: - | -- {% if curve.squarefree %} - yes - {% elif curve.squarefree is not none %} - no - {% else %} - not computed - {% endif %} - | -
| {{ KNOWL('modcurve.decomposition', 'Decomposition') }}: | {{ curve.formatted_dims }} |
| {{ KNOWL('modcurve.decomposition', 'Newforms') }}: | {{ curve.formatted_newforms | safe }} |
| {{ KNOWL('ag.conductor', 'Conductor') }}: | ${{ curve.factored_conductor }}$ | +
| {{ KNOWL('av.simple', 'Simple') }}: | ++ {% if curve.simple %} + yes + {% elif curve.simple is not none %} + no + {% else %} + not computed + {% endif %} + | +
| {{ KNOWL('av.squarefree', 'Squarefree') }}: | ++ {% if curve.squarefree %} + yes + {% elif curve.squarefree is not none %} + no + {% else %} + not computed + {% endif %} + | +
| {{ KNOWL('modcurve.decomposition', 'Decomposition') }}: | {{ curve.formatted_dims }} | +
| {{ KNOWL('modcurve.decomposition', 'Newforms') }}: | {{ curve.formatted_newforms | safe }} | +
{{ KNOWL('ag.canonical_model', 'Canonical model') }} in $\mathbb{P}^{ {{nb_var-1}} }$:
-{% elif type == 2 %} -{% if smooth == True %} - {{ KNOWL('modcurve.plane_model', 'Smooth plane model') }}: - {% elif smooth == False %} - {{ KNOWL('modcurve.plane_model', 'Singular plane model') }}: - {% else %} - {{ KNOWL('modcurve.plane_model', 'Plane model') }}: - {% endif %} -
-{% elif type == 5 %} -{% if curve.genus == 1 %} - {{ KNOWL('ec.weierstrass_coeffs', 'Weierstrass model') }}: - {% else %} - {{ KNOWL('ag.hyperelliptic_curve', 'Weierstrass model') }}: +
{{ KNOWL('ag.canonical_model', 'Canonical model') }} in $\mathbb{P}^{ {{nb_var-1}} }$:
+ {% elif type == 2 %} +{% if smooth == True %} + {{ KNOWL('modcurve.plane_model', 'Smooth plane model') }}: + {% elif smooth == False %} + {{ KNOWL('modcurve.plane_model', 'Singular plane model') }}: + {% else %} + {{ KNOWL('modcurve.plane_model', 'Plane model') }}: + {% endif %} +
+ {% elif type == 5 %} +{% if curve.genus == 1 %} + {{ KNOWL('ec.weierstrass_coeffs', 'Weierstrass model') }}: + {% else %} + {{ KNOWL('ag.hyperelliptic_curve', 'Weierstrass model') }}: + {% endif %} +
+ {% elif type == 7 %} +{{ KNOWL('ag.hyperelliptic_curve', 'Geometric Weierstrass model') }}:
+ {% elif type == 8 %} +{{ KNOWL('modcurve.embedded_model', 'Embedded model') }} in $\mathbb{P}^{ {{nb_var-1}} } $:
+ {% endif %} +| $ {{ lines[0] }}$ | +$=$ | +$ {{ lines[1] }}$ | +
| ${{ lines[2] }}$ | +$=$ | +${{ lines[3] }}$ | +
| + | $=$ | +${{ line }}$ | +
| + | $=$ | +${{ lines[2] }}$ | +
| + | + | Show {{ (lines|length) - 3 }} more equations | +
This modular curve is isomorphic to $\mathbb{P}^1$.
{% endif %} - -{% elif type == 7 %} -{{ KNOWL('ag.hyperelliptic_curve', 'Geometric Weierstrass model') }}:
-{% elif type == 8 %} -{{ KNOWL('modcurve.embedded_model', 'Embedded model') }} in $\mathbb{P}^{ {{nb_var-1}} } $:
-{% endif %} -| $ {{ lines[0] }}$ | -$=$ | -$ {{ lines[1] }}$ | -
| ${{ lines[2] }}$ | -$=$ | -${{ lines[3] }}$ | -
| - | $=$ | -${{ line }}$ | -
| - | $=$ | -${{ lines[2] }}$ | -
| - | - | Show {{ (lines|length) - 3 }} more equations | -
This modular curve is isomorphic to $\mathbb{P}^1$.
-{% endif %} -{% if curve.has_more_models %} -Some stored models are too large to be displayed and are available for download.
-{% endif %} {% endif %}{{curve.rational_points_description | safe}}
{% if (curve.genus > 1 or curve.genus == 1 and curve.rank == 0) and curve.db_rational_points %} -| {{ KNOWL('ec.q.lmfdb_label', 'Elliptic curve') }} | {{ KNOWL('ec.complex_multiplication', 'CM') }} | {{ KNOWL('ec.q.j_invariant', '$j$-invariant') }} | {{ KNOWL('nf.weil_height', '$j$-height') }} | {{ curve.rational_point_coord_headers |safe}}|
|---|---|---|---|---|
| {% if url %}{{label}}{% endif %} | {{ cm | safe}} | {{jinv | safe}} | {{jfac | safe}} | ${{"%.3f"%jheight}}$ | {{coords | safe}}
| {{ KNOWL('ec.q.lmfdb_label', 'Elliptic curve') }} | +{{ KNOWL('ec.complex_multiplication', 'CM') }} | +{{ KNOWL('ec.q.j_invariant', '$j$-invariant') }} | +{{ KNOWL('nf.weil_height', '$j$-height') }} | {{ curve.rational_point_coord_headers |safe}} +|
|---|---|---|---|---|
| {% if url %}{{label}}{% endif %} | +{{ cm | safe}} | {{jinv | safe}} | +{{jfac | safe}} | ${{"%.3f"%jheight}}$ | {{coords | safe}} +
{{ curve.low_degree_points_description | safe }}
{% if (curve.genus > 1 or curve.genus == 1 and curve.rank == 0) and curve.db_nf_points %} -| {{ KNOWL('modcurve.point_degree', 'Degree') }} | {{ KNOWL('modcurve.point_residue_field', 'Residue field') }} | {{ KNOWL('ec.j_invariant', '$j$-invariant') }} | {{ KNOWL('ec.j_invariant', '$\\Q(j)$') }} | {{ KNOWL('nf.weil_height', '$j$-height') }} | {{ KNOWL('ec.complex_multiplication', 'CM') }} | {{ KNOWL('ag.isolated_point', 'Isolated') }} | {% if not curve.contains_negative_one %}{{ KNOWL('ec.curve_label', 'Elliptic Curve') }} | {% endif %}{{curve.nf_point_coord_headers|safe}}
|---|---|---|---|---|---|---|---|
| ${{degree}}$ | {{res_field | safe}} | {{jinv | safe}} | {{j_field | safe}} | ${{"%.3f"%j_height}}$ | {{ cm | safe}} | {{isolated | safe}} | {% if not curve.contains_negative_one %}{{ec_label}} | {% endif %}{{coords | safe}}
| {{ KNOWL('modcurve.point_degree', 'Degree') }} | {{ KNOWL('modcurve.point_residue_field', 'Residue field') }} | {{curve.nf_point_coord_headers|safe}}||||||
| ${{degree}}$ | {{res_field | safe}} | {{coords | safe}}
| {{ KNOWL('modcurve.point_degree', 'Degree') }} | +{{ KNOWL('modcurve.point_residue_field', 'Residue field') }} | +{{ KNOWL('ec.j_invariant', '$j$-invariant') }} | +{{ KNOWL('ec.j_invariant', '$\\Q(j)$') }} | {{ KNOWL('nf.weil_height', '$j$-height') }} | {{ KNOWL('ec.complex_multiplication', 'CM') }} | +{{ KNOWL('ag.isolated_point', 'Isolated') }} | + {% if not curve.contains_negative_one %} +{{ KNOWL('ec.curve_label', 'Elliptic Curve') }} | + {% endif %} + {{curve.nf_point_coord_headers|safe}} +
|---|---|---|---|---|---|---|---|
| ${{degree}}$ | +{{res_field | safe}} | +{{jinv | safe}} | +{{j_field | safe}} | +${{"%.3f"%j_height}}$ | +{{ cm | safe}} | +{{isolated | safe}} | + {% if not curve.contains_negative_one %} +{{ec_label}} | + {% endif %} + {{coords | safe}} +
| {{ KNOWL('modcurve.point_degree', 'Degree') }} | +{{ KNOWL('modcurve.point_residue_field', 'Residue field') }} | {{curve.nf_point_coord_headers|safe}} +||||||
| ${{degree}}$ | +{{res_field | safe}} | + {{coords | safe}} +
Birational map from {{ curve.model_type_str(domain_model_type) }} to {{ curve.model_type_str(codomain_model_type) }}:
-| $\displaystyle {{ coord }}$ | -$=$ | -$\displaystyle {{ eq }}$ | -
| $\displaystyle {{ coord }}$ | +$=$ | +$\displaystyle {{ eq }}$ | +
- {% if codomain_label == "1.1.0.a.1" and codomain_model_type == 4 %} - where the projective coordinates $(E_4:E_6)$ of weights $4$ and $6$ are as follows - {% else %} - {% if codomain_label == "1.1.0.a.1" and codomain_model_type == 1 %} - {{ KNOWL('modcurve.j_invariant_map', '$j$-invariant map') }} - {% else %} - Map - {% endif %} - of degree {{degree}} {{ curve.model_type_domain(domain_model_type) }} to {{ curve.model_type_codomain(codomain_model_type) }} the modular curve - {% if codomain_name %} - {{name_to_latex(codomain_name)}} - {% else %} - {{codomain_label}} - {% endif %} - {% if codomain_model_type == 1 and codomain_label != "1.1.0.a.1" %} - isomorphic to $P^1$ +
+ {% if codomain_label == "1.1.0.a.1" and codomain_model_type == 4 %} + where the projective coordinates $(E_4:E_6)$ of weights $4$ and $6$ are as follows + {% else %} + {% if codomain_label == "1.1.0.a.1" and codomain_model_type == 1 %} + {{ KNOWL('modcurve.j_invariant_map', '$j$-invariant map') }} + {% else %} + Map + {% endif %} + of degree {{degree}} {{ curve.model_type_domain(domain_model_type) }} to {{ curve.model_type_codomain(codomain_model_type) }} the modular curve + {% if codomain_name %} + {{name_to_latex(codomain_name)}} + {% else %} + {{codomain_label}} + {% endif %} + {% if codomain_model_type == 1 and codomain_label != "1.1.0.a.1" %} + isomorphic to $P^1$ + {% endif %} + {% endif %} + :
+| $\displaystyle {{ coord }}$ | +$=$ | +$\displaystyle {{ eq }}$ | +
Equation of the image curve:
+| ${{codomain_equation[0]}}$ | +$=$ | +$ {{codomain_equation[1]}} $ | +
| + | $=$ | +$ {{line}} $ | +
Some stored maps are too large to be displayed and are available for download.
{% endif %} - : -| $\displaystyle {{ coord }}$ | -$=$ | -$\displaystyle {{ eq }}$ | -
Equation of the image curve:
-| ${{codomain_equation[0]}}$ | -$=$ | -$ {{codomain_equation[1]}} $ | -
| - | $=$ | -$ {{line}} $ | -
Some stored maps are too large to be displayed and are available for download.
-{% endif %} {% endif %} {% if curve.fiber_product_of or curve.modular_covers or curve.modular_covered_by %} -| - - |
Cover information
Click on a modular curve in the diagram to see information about it.
- |
-
| + + |
+ Cover information+
+ Click on a modular curve in the diagram to see information about it.
+
+ |
+
The following {{ KNOWL('modcurve.modular_cover','modular covers') }} realize this modular curve as a {{ KNOWL('modcurve.fiber_product','fiber product') }} over $X(1)$. -
| {{ KNOWL('modcurve.modular_cover','Factor curve') }} | -{{ KNOWL('modcurve.level','Level') }} | -{{ KNOWL('modcurve.relative_index', 'Index') }} | -{{ KNOWL('modcurve.modular_cover','Degree') }} | -{{ KNOWL('modcurve.genus','Genus') }} | -{{ KNOWL('modcurve.rank','Rank') }} | - {% if curve.dims %} -{{ KNOWL('modcurve.modular_cover','Kernel decomposition') }} | - {% endif %} -|
|---|---|---|---|---|---|---|---|
| {{disp}} | -${{ level }}$ | -${{ index }}$ | -${{ degree }}$ | -${{ genus }}$ | -${{ rank }}$ | - {% if curve.dims %} - {% if genus > 0 %} -{{ kernel if kernel else "dimension zero" | safe }} | - {% elif curve.genus > 0 %} -full Jacobian | - {% endif %} - {% endif %} -
The following {{ KNOWL('modcurve.modular_cover','modular covers') }} realize this modular curve as a {{ KNOWL('modcurve.fiber_product','fiber product') }} over $X(1)$. +
| {{ KNOWL('modcurve.modular_cover','Factor curve') }} | +{{ KNOWL('modcurve.level','Level') }} | +{{ KNOWL('modcurve.relative_index', 'Index') }} | +{{ KNOWL('modcurve.modular_cover','Degree') }} | +{{ KNOWL('modcurve.genus','Genus') }} | +{{ KNOWL('modcurve.rank','Rank') }} | + {% if curve.dims %} +{{ KNOWL('modcurve.modular_cover','Kernel decomposition') }} | + {% endif %} +|
|---|---|---|---|---|---|---|---|
| {{disp}} | +${{ level }}$ | +${{ index }}$ | +${{ degree }}$ | +${{ genus }}$ | +${{ rank }}$ | + {% if curve.dims %} + {% if genus > 0 %} +{{ kernel if kernel else "dimension zero" | safe }} | + {% elif curve.genus > 0 %} +full Jacobian | + {% endif %} + {% endif %} +
This modular curve {{ KNOWL('modcurve.modular_cover','minimally covers') }} the modular curves listed below. -
| {{ KNOWL('modcurve.modular_cover','Covered curve') }} | -{{ KNOWL('modcurve.level','Level') }} | -{{ KNOWL('modcurve.relative_index', 'Index') }} | -{{ KNOWL('modcurve.modular_cover','Degree') }} | -{{ KNOWL('modcurve.genus','Genus') }} | -{{ KNOWL('modcurve.rank','Rank') }} | - {% if curve.dims %} -{{ KNOWL('modcurve.modular_cover','Kernel decomposition') }} | - {% endif %} -|
|---|---|---|---|---|---|---|---|
| {{disp}} | -${{ level }}$ | -${{ index }}$ | -${{ degree }}$ | -${{ genus }}$ | -${{ rank }}$ | - {% if curve.dims %} - {% if genus > 0 %} -{{ kernel if kernel else "dimension zero" | safe }} | - {% elif curve.genus > 0 %} -full Jacobian | - {% endif %} - {% endif %} -
This modular curve {{ KNOWL('modcurve.modular_cover','minimally covers') }} the modular curves listed below. +
| {{ KNOWL('modcurve.modular_cover','Covered curve') }} | +{{ KNOWL('modcurve.level','Level') }} | +{{ KNOWL('modcurve.relative_index', 'Index') }} | +{{ KNOWL('modcurve.modular_cover','Degree') }} | +{{ KNOWL('modcurve.genus','Genus') }} | +{{ KNOWL('modcurve.rank','Rank') }} | + {% if curve.dims %} +{{ KNOWL('modcurve.modular_cover','Kernel decomposition') }} | + {% endif %} +|
|---|---|---|---|---|---|---|---|
| {{disp}} | +${{ level }}$ | +${{ index }}$ | +${{ degree }}$ | +${{ genus }}$ | +${{ rank }}$ | + {% if curve.dims %} + {% if genus > 0 %} +{{ kernel if kernel else "dimension zero" | safe }} | + {% elif curve.genus > 0 %} +full Jacobian | + {% endif %} + {% endif %} +
This modular curve is {{ KNOWL('modcurve.modular_cover','minimally covered by') }} the modular curves in the database listed below. -
| {{ KNOWL('modcurve.modular_cover','Covering curve') }} | -{{ KNOWL('modcurve.level','Level') }} | -{{ KNOWL('modcurve.relative_index', 'Index') }} | -{{ KNOWL('modcurve.modular_cover','Degree') }} | -{{ KNOWL('modcurve.genus','Genus') }} | - {% if curve.dims %} -{{ KNOWL('modcurve.rank','Rank') }} | -{{ KNOWL('modcurve.modular_cover','Kernel decomposition') }} | - {% endif %} -
|---|---|---|---|---|---|---|
| {{disp}} | -${{ level }}$ | -${{ index }}$ | -${{ degree }}$ | -${{ genus }}$ | - {% if curve.dims %} -${{ rank }}$ | -{{ kernel if kernel else "dimension zero" | safe }} | - {% endif %} -
This modular curve is {{ KNOWL('modcurve.modular_cover','minimally covered by') }} the modular curves in the database listed below. +
| {{ KNOWL('modcurve.modular_cover','Covering curve') }} | +{{ KNOWL('modcurve.level','Level') }} | +{{ KNOWL('modcurve.relative_index', 'Index') }} | +{{ KNOWL('modcurve.modular_cover','Degree') }} | +{{ KNOWL('modcurve.genus','Genus') }} | + {% if curve.dims %} +{{ KNOWL('modcurve.rank','Rank') }} | +{{ KNOWL('modcurve.modular_cover','Kernel decomposition') }} | + {% endif %} +
|---|---|---|---|---|---|---|
| {{disp}} | +${{ level }}$ | +${{ index }}$ | +${{ degree }}$ | +${{ genus }}$ | + {% if curve.dims %} +${{ rank }}$ | +{{ kernel if kernel else "dimension zero" | safe }} | + {% endif %} +