Hyperelliptic Curves: Operations on the Jacobian over $\mbox{\bf Q}$

Most of the functions listed here apply only in the case of Jacobians of genus 2 curves.

• Order of a point
• Height constant, canonical heights, naive height
• Height pairing matrix and regulator
• Enumeration of all $\mbox{\bf Q}$-rational points up to a given height bound (Elkies-Stahlke-Stoll method)
• 2-Selmer rank (via 2-descent)
• 2-torsion subgroup, full torsion subgroup
• Rank of the subgroup of the Mordell-Weil group generated by a given set of points on the Jacobian
• Chabauty's method for determining rational points on a curve over Q with Mordell-Weil rank at most 1