show · g2c.has_square_sha all knowls · up · search:

The order of the Tate-Shafarevich group of the Jacobian of a curve is either a square, or twice a square, assuming it is finite; this is a theorem of Poonen and Stoll [arXiv:math/9911267 , 10.2307/121064 ].

For elliptic curves, only the square case can occur, but for Jacobians of genus 2 curves, both cases are known to occur.

Authors:
Knowl status:
• Review status: reviewed
• Last edited by Andrew Sutherland on 2020-10-09 18:21:28
Referred to by:
History:
Differences