Arithmetic Study Group: On families of n-congruent elliptic curves
14 November 2017 14:00 in CM 219
Elliptic curves E and E' are said to be n-congruent if their
n-torsion subgroups are isomorphic as Galois modules. The elliptic curves
n-congruent to a given elliptic curve are parametrised by (the
non-cuspidal points of) certain twists of the modular curve X(n). I will
discuss methods for computing equations for these curves, and also for the
surfaces that parametrise pairs of n-congruent elliptic curves.