Fix error in torsion_bounds function for elliptic curves #39620
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Fixes #39580. As pointed out in #39580, the
torsion_bounds
method of elliptic curves has a bug in its handling of the situation where the monic defining polynomial of the number field has nontrivial denominators in some of its coefficients.Diagnosis. Assume
E
is an elliptic curve over a number fieldK
, and letf
be a monic defining polynomial ofK
, so a roota_
off
generatesK
. The code fortorsion_bounds
replacesf
with a different polynomial (still calledf
, but obtained by rescaling the variable) that is monic and integral. The code erroneously assumes thata_
is a root of this new polynomial. To fix this, we can rescale a root of the new polynomial, to obtain a root of the original one.📝 Checklist
⌛ Dependencies