- Plane curve constructors
- Affine plane curves over a general ring
- Projective plane curves over a general ring
- Plane conic constructor
- Projective plane conics over a field
- Projective plane conics over a number field
- Projective plane conics over \(\QQ\)
- Projective plane conics over finite fields
- Projective plane conics over prime finite fields
- Elliptic curve constructor
- Construct Elliptic Curves as Jacobians
- 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 \(\QQ\))
- Local data for elliptic curves over number fields
- Kodaira symbols
- Isomorphisms between Weierstrass models of elliptic curves
- Isogenies
- Isogenies of small prime degree.
- Weierstrass \(\wp\) function for elliptic curves
- Period lattices of elliptic curves and related functions
- Formal groups of elliptic curves
- Tate’s parametrisation of \(p\)-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 \(\QQ\)
- Galois representations attached to elliptic curves
- Tate-Shafarevich group
- Miscellaneous p-adic functions
- Complex multiplication for elliptic curves

- Hyperelliptic curve constructor
- Hyperelliptic curves over a finite field
- Hyperelliptic curves over a general ring
- Mestre’s algorithm
- 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