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Sage Reference Manual

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1
Plane curves

2
=========================

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.. toctree::

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   :maxdepth: 2

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   sage/schemes/plane_curves/constructor

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   sage/schemes/plane_curves/affine_curve

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   sage/schemes/plane_curves/projective_curve

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   sage/schemes/plane_curves/curve

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   sage/schemes/plane_conics/constructor

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   sage/schemes/plane_conics/con_field

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   sage/schemes/plane_conics/con_number_field

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   sage/schemes/plane_conics/con_rational_field

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   sage/schemes/plane_conics/con_finite_field

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   sage/schemes/plane_conics/con_prime_finite_field

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   sage/schemes/jacobians/abstract_jacobian

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Plane quartics

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=========================

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.. toctree::

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   :maxdepth: 2

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   sage/schemes/plane_quartics/quartic_constructor

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   sage/schemes/plane_quartics/quartic_generic

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31
Elliptic curves

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=========================

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34
.. toctree::

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   :maxdepth: 2

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   sage/schemes/elliptic_curves/constructor

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   sage/schemes/elliptic_curves/jacobian

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   sage/schemes/elliptic_curves/ell_point

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   sage/schemes/elliptic_curves/ell_generic

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   sage/schemes/elliptic_curves/ell_field

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   sage/schemes/elliptic_curves/ell_finite_field

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   sage/schemes/elliptic_curves/formal_group

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45
Maps between them

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.. toctree::

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   :maxdepth: 2

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   sage/schemes/elliptic_curves/weierstrass_morphism

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   sage/schemes/elliptic_curves/ell_curve_isogeny

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   sage/schemes/elliptic_curves/isogeny_small_degree

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55
Elliptic curves over number fields

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----------------------------------

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.. toctree::

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   :maxdepth: 2

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   sage/schemes/elliptic_curves/ell_rational_field

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   sage/schemes/elliptic_curves/ec_database

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   sage/schemes/elliptic_curves/ell_number_field

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   sage/schemes/elliptic_curves/height

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   sage/schemes/elliptic_curves/ell_torsion

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   sage/schemes/elliptic_curves/gal_reps

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   sage/schemes/elliptic_curves/gal_reps_number_field

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   sage/schemes/elliptic_curves/isogeny_class

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   sage/schemes/elliptic_curves/sha_tate

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   sage/schemes/elliptic_curves/cm

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75


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The following relate to elliptic curves over local nonarchimedean fields.

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.. toctree::

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   :maxdepth: 2

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   sage/schemes/elliptic_curves/ell_local_data

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   sage/schemes/elliptic_curves/kodaira_symbol

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   sage/schemes/elliptic_curves/ell_tate_curve

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   sage/schemes/elliptic_curves/padics

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Analytic properties over `\CC`.

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.. toctree::

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   :maxdepth: 2

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   sage/schemes/elliptic_curves/ell_wp

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   sage/schemes/elliptic_curves/period_lattice

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   sage/schemes/elliptic_curves/period_lattice_region

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Modularity and `L`-series over `\QQ`.

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.. toctree::

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   :maxdepth: 2

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   sage/schemes/elliptic_curves/modular_parametrization

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   sage/schemes/elliptic_curves/ell_modular_symbols

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   sage/schemes/elliptic_curves/lseries_ell

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   sage/schemes/elliptic_curves/heegner

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   sage/schemes/elliptic_curves/padic_lseries

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To be sorted

107
------------

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109
.. toctree::

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   :maxdepth: 2

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112
   sage/schemes/elliptic_curves/descent_two_isogeny

113
   sage/schemes/elliptic_curves/ell_egros

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   sage/schemes/elliptic_curves/ell_padic_field

115
   sage/schemes/elliptic_curves/gp_simon

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   sage/schemes/elliptic_curves/mod5family

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   sage/schemes/elliptic_curves/weierstrass_transform

118


119
.. Not included because prove_BSD is bound in ell_rational_field, leading to duplicate citations

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.. sage/schemes/elliptic_curves/BSD

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Hyperelliptic curves

123
====================

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125
.. toctree::

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   :maxdepth: 2

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128
   sage/schemes/hyperelliptic_curves/constructor

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   sage/schemes/hyperelliptic_curves/hyperelliptic_generic

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   sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field

131
   sage/schemes/hyperelliptic_curves/hyperelliptic_padic_field

132
   sage/schemes/hyperelliptic_curves/hyperelliptic_rational_field

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134
   sage/schemes/hyperelliptic_curves/mestre

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136
   sage/schemes/hyperelliptic_curves/monsky_washnitzer

137
   sage/schemes/hyperelliptic_curves/hypellfrob

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   sage/schemes/hyperelliptic_curves/jacobian_generic

140
   sage/schemes/hyperelliptic_curves/jacobian_g2

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   sage/schemes/hyperelliptic_curves/jacobian_homset

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   sage/schemes/hyperelliptic_curves/jacobian_morphism

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   sage/schemes/hyperelliptic_curves/hyperelliptic_g2_generic

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   sage/schemes/hyperelliptic_curves/hyperelliptic_g2_finite_field

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   sage/schemes/hyperelliptic_curves/hyperelliptic_g2_padic_field

147
   sage/schemes/hyperelliptic_curves/hyperelliptic_g2_rational_field

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   sage/schemes/hyperelliptic_curves/invariants

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   sage/schemes/hyperelliptic_curves/kummer_surface

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151
   sage/interfaces/genus2reduction

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.. include:: ../footer.txt

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