On the Diophantine equation
On a theorem of Mestre and Schoof
A well known theorem of Mestre and Schoof implies that the order of an elliptic curve over a prime field can be uniquely determined by computing the orders of a few points on and its quadratic twist, provided that . We extend this result to all finite fields with , and all prime fields with .
Computing periods of cusp forms and modular elliptic curves.
Visualizing elements in the Shafarevich-Tate group.
Page 1