- 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

Maps between them

- Elliptic curves over the rational numbers
- Tables of elliptic curves of given rank
- Elliptic curves over number fields
- Canonical heights for elliptic curves over number fields
- Torsion subgroups of elliptic curves over number fields (including \(\QQ\))
- Galois representations attached to elliptic curves
- Galois representations for elliptic curves over number fields.
- Tate-Shafarevich group
- Complex multiplication for elliptic curves

The following relate to elliptic curves over local nonarchimedean fields.

Analytic properties over \(\CC\).

Modularity and \(L\)-series over \(\QQ\).

- Hyperelliptic curve constructor
- Hyperelliptic curves over a finite field
- Hyperelliptic curves over a general ring
- Mestre’s algorithm
- Computation of Frobenius matrix on Monsky-Washnitzer cohomology
- 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