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implement Bröker's algorithm for constructing supersingular curves #36665

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merged 3 commits into from
Dec 10, 2023

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@yyyyx4 yyyyx4 commented Nov 6, 2023

In this patch, we add a function special_supersingular_curve() to construct a supersingular elliptic curve defined over a given $\mathbb F_p$ having a small-degree endomorphism which anticommutes with Frobenius. The function optionally constructs and returns the endomorphism as an explicit isogeny; this should prove useful later when we have better tools for endomorphism rings.

Bröker's algorithm is both the standard approach for finding a supersingular elliptic curve in given characteristic, as well as part of the setup for several algorithms dealing with endomorphism rings: The special endomorphism together with Frobenius forms a generating set of the endomorphism algebra.

Cc: @JohnCremona @defeo @GiacomoPope @remyoudompheng

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I amde a couple of comments, not in a formal review (yet).

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yyyyx4 commented Nov 22, 2023

Thank you!

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vbraun commented Dec 5, 2023

pdf docs fail

[sagemath_doc_pdf-none] Overfull \hbox
[sagemath_doc_pdf-none] ! Undefined control sequence.
[sagemath_doc_pdf-none] l.12331 has coefficients in \(\FF
[sagemath_doc_pdf-none]                                  _p\);

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github-actions bot commented Dec 6, 2023

Documentation preview for this PR (built with commit 1e06b22; changes) is ready! 🎉

@vbraun vbraun merged commit 2051800 into sagemath:develop Dec 10, 2023
13 of 17 checks passed
@mkoeppe mkoeppe added this to the sage-10.3 milestone Dec 10, 2023
@yyyyx4 yyyyx4 deleted the public/bröker branch December 20, 2023 15:22
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4 participants