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For an elliptic curve defined over $\Q$ of rank $0$ or $1$, the analytic order of Ш is known to be rational, and has been computed exactly; in all cases the computed value is an integer. For curves of rank at least $2$, the value computed is not known to be rational, let alone integral, though in all cases the computed value is always close to an integer, and we store and display the rounded value.

Knowl status:
  • Review status: reviewed
  • Last edited by John Cremona on 2019-02-08 10:59:20
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