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.

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- Last edited by Andrew Sutherland on 2020-10-09 18:21:28

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- 2020-10-09 18:21:28 by Andrew Sutherland (Reviewed)
- 2020-10-09 18:20:23 by Andrew Sutherland
- 2020-10-09 18:19:14 by Andrew Sutherland
- 2020-10-09 18:18:40 by Andrew Sutherland
- 2020-01-07 06:14:59 by Andrew Sutherland (Reviewed)
- 2020-01-06 17:11:14 by Andrew Sutherland
- 2018-05-23 16:56:15 by John Cremona (Reviewed)

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