implement Bröker's algorithm for constructing supersingular curves #36665
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JohnCremona
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Nov 16, 2023
JohnCremona
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Nov 16, 2023
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I amde a couple of comments, not in a formal review (yet). |
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JohnCremona
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Thank you! |
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Documentation preview for this PR (built with commit 1e06b22; changes) is ready! 🎉 |
vbraun
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Oct 9, 2024
…lar_curve()
This is a follow-up to sagemath#36665: There, a CM endomorphism is chosen
automatically to construct a "special" supersingular elliptic curve. In
some applications, it can be useful to explicitly supply the desired
degree of such an endomorphism to Bröker's algorithm, which is made
possible by this patch.
Note that some of the subroutines used in the new code paths are
relatively fragile, which can cause the functionality added here to fail
for some inputs, but this has been documented in the appropriate places.
URL: sagemath#38483
Reported by: Lorenz Panny
Reviewer(s): Giacomo Pope, Lorenz Panny
vbraun
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Oct 11, 2024
…lar_curve()
This is a follow-up to sagemath#36665: There, a CM endomorphism is chosen
automatically to construct a "special" supersingular elliptic curve. In
some applications, it can be useful to explicitly supply the desired
degree of such an endomorphism to Bröker's algorithm, which is made
possible by this patch.
Note that some of the subroutines used in the new code paths are
relatively fragile, which can cause the functionality added here to fail
for some inputs, but this has been documented in the appropriate places.
URL: sagemath#38483
Reported by: Lorenz Panny
Reviewer(s): Giacomo Pope, Lorenz Panny
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In this patch, we add a function$\mathbb F_p$ 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.
special_supersingular_curve()to construct a supersingular elliptic curve defined over a givenBröker'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