compute endomorphism orders for elliptic curves over finite fields (rank-2 case) #38493
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I'll look at this tomorrow. I did implement a special case of Sutherland 's algorithm already for our CM testing algorithm last year. |
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Thank you! I think the implementation you wrote is the function I'm calling here. I just extended it to work for the supersingular case, too. |
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Apologies to @yyyyx4 for promising and then not delivering -- sheer forgetfulness on my part. I cannot promise to be able to review this in the next several days. Feel free to send me reminders. |
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Documentation preview for this PR (built with commit 284dbfa; changes) is ready! 🎉 |
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No worries, @JohnCremona! I do think it would be nice to get this into the next release, but it is by no means urgent. |
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| # classes of curves instead. | ||
| E0 = [self] * 3 | ||
| E1 = [phi.codomain() for phi in self.isogenies_prime_degree(ell)] | ||
| assert E1 |
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I don't think that including assert statements is good practice for production code (though of course essential while testing). Does the developers' guide say something about this? But the alternative would be to test the condition anyway and raise an error if it fails, so perhaps it does not make much difference. (Laos, I am sure thta my own code in Sage does include assert statements...)
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I don't think there are any rules about it. I left these in since they are very quick sanity checks that might detect if something is really wrong with the algorithm. Exceptions are for a different purpose; they communicate errors that can occur as part of the expected functionality of the code (e.g., invalid inputs). In my opinion, there should be assertions all over the code base anyway, with the default in production environments being that they are turned off (python -O or PYTHONOPTIMIZE=1), but that's a different discussion...
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Thanks for the review, @JohnCremona! If you are happy with my latest changes, don't forget to approve the pull request (I think I can no longer set "positive review" myself, contrary to the old Trac days). |
sagemathgh-38493: compute endomorphism orders for elliptic curves over finite fields (rank-2 case) For an elliptic curve E over a finite field with an endomorphism algebra of rank two over ℚ, the endomorphism ring is a superorder of the "Frobenius order" ℤ[π]. This patch adds a simple method to compute the exact imaginary-quadratic order containing ℤ[π] which is isomorphic to the endomorphism ring of the curve, and generalizes the algorithm to supersingular elliptic curves with a (rational) endomorphism algebra of rank 2. URL: sagemath#38493 Reported by: Lorenz Panny Reviewer(s): John Cremona, Lorenz Panny
sagemathgh-38493: compute endomorphism orders for elliptic curves over finite fields (rank-2 case) For an elliptic curve E over a finite field with an endomorphism algebra of rank two over ℚ, the endomorphism ring is a superorder of the "Frobenius order" ℤ[π]. This patch adds a simple method to compute the exact imaginary-quadratic order containing ℤ[π] which is isomorphic to the endomorphism ring of the curve, and generalizes the algorithm to supersingular elliptic curves with a (rational) endomorphism algebra of rank 2. URL: sagemath#38493 Reported by: Lorenz Panny Reviewer(s): John Cremona, Lorenz Panny
sagemathgh-38493: compute endomorphism orders for elliptic curves over finite fields (rank-2 case) For an elliptic curve E over a finite field with an endomorphism algebra of rank two over ℚ, the endomorphism ring is a superorder of the "Frobenius order" ℤ[π]. This patch adds a simple method to compute the exact imaginary-quadratic order containing ℤ[π] which is isomorphic to the endomorphism ring of the curve, and generalizes the algorithm to supersingular elliptic curves with a (rational) endomorphism algebra of rank 2. URL: sagemath#38493 Reported by: Lorenz Panny Reviewer(s): John Cremona, Lorenz Panny
sagemathgh-38493: compute endomorphism orders for elliptic curves over finite fields (rank-2 case) For an elliptic curve E over a finite field with an endomorphism algebra of rank two over ℚ, the endomorphism ring is a superorder of the "Frobenius order" ℤ[π]. This patch adds a simple method to compute the exact imaginary-quadratic order containing ℤ[π] which is isomorphic to the endomorphism ring of the curve, and generalizes the algorithm to supersingular elliptic curves with a (rational) endomorphism algebra of rank 2. URL: sagemath#38493 Reported by: Lorenz Panny Reviewer(s): John Cremona, Lorenz Panny
sagemathgh-38493: compute endomorphism orders for elliptic curves over finite fields (rank-2 case) For an elliptic curve E over a finite field with an endomorphism algebra of rank two over ℚ, the endomorphism ring is a superorder of the "Frobenius order" ℤ[π]. This patch adds a simple method to compute the exact imaginary-quadratic order containing ℤ[π] which is isomorphic to the endomorphism ring of the curve, and generalizes the algorithm to supersingular elliptic curves with a (rational) endomorphism algebra of rank 2. URL: sagemath#38493 Reported by: Lorenz Panny Reviewer(s): John Cremona, Lorenz Panny
For an elliptic curve E over a finite field with an endomorphism algebra of rank two over ℚ, the endomorphism ring is a superorder of the "Frobenius order" ℤ[π].
This patch adds a simple method to compute the exact imaginary-quadratic order containing ℤ[π] which is isomorphic to the endomorphism ring of the curve, and generalizes the algorithm to supersingular elliptic curves with a (rational) endomorphism algebra of rank 2.