Elliptic and Plane Curves

• Plane curve constructors
• Affine plane curves over a general ring
• Projective plane curves over a general ring
• Elliptic curve constructor
• Elliptic curves over a general ring.
• Elliptic curves over a general field
• Elliptic curves over the rational numbers
• Heegner points on elliptic curves over the rational numbers
• Tables of elliptic curves of given rank
• Elliptic curves over number fields.
• Elliptic curves over finite fields
• Points on elliptic curves
• Torsion subgroups of elliptic curves over number fields (including ).
• Local data for elliptic curves over number fields
• Kodaira symbols.
• Isomorphisms between Weierstrass models of elliptic curves
• Isogenies
• Weierstrass function for elliptic curves.
• Period lattices of elliptic curves and related functions.
• Formal groups of elliptic curves.
• Tate’s parametrisation of -adic curves with multiplicative reduction
• Computation of Frobenius matrix on Monsky-Washnitzer cohomology.
• p-adic L-functions of elliptic curves
• Modular symbols
• Modular parametrization of elliptic curves over .
• Galois representations attached to elliptic curves
• Tate-Shafarevich group
• Miscellaneous p-adic functions
• Complex multiplication for elliptic curves

Hyperelliptic Curves

• Hyperelliptic curve constructor
• Hyperelliptic curves over a finite field
• Hyperelliptic curves over a general ring
• Constructor for Jacobian of a hyperelliptic curve
• Jacobian of a Hyperelliptic curve of Genus 2.
• Jacobian of a General Hyperelliptic Curve
• Rational point sets on a Jacobian
• Jacobian ‘morphism’ as a class in the Picard group.
• Conductor and Reduction Types for Genus 2 Curves