Noam Elkies: Families of genus-2 curves with 5-torsion

14th July, 2023
Watch Later Cinema Mode

We give birational parametrizations of pairs (C,T) where T is a 5-torsion point on the Jacobian of a genus-2 curve C, possibly satisfying one or more of the following additional conditions:

  • T = (P) – (P0) for some points P0, P in C with P0 Weierstrass;
  • C has one or more additional rational Weierstrass points;
  • Jac(C) has real multiplication by (1+√5)/2, and T is a √5-torsion point.

This video (which is better viewed on Panopto, here) was produced by ICERM at Brown University, as part of the conference LMFDB, Computation and Number Theory.