From 287a90c87272956fdff833b809a1b64b06ce4216 Mon Sep 17 00:00:00 2001 From: Lorenz Panny Date: Thu, 24 Nov 2022 14:06:46 +0800 Subject: [PATCH] add another example for .twists() --- src/sage/schemes/elliptic_curves/ell_finite_field.py | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/src/sage/schemes/elliptic_curves/ell_finite_field.py b/src/sage/schemes/elliptic_curves/ell_finite_field.py index 479059f0898..71f5c316734 100644 --- a/src/sage/schemes/elliptic_curves/ell_finite_field.py +++ b/src/sage/schemes/elliptic_curves/ell_finite_field.py @@ -1411,6 +1411,17 @@ def twists(self): Elliptic Curve defined by y^2 = x^3 + ... over Finite Field of size 97, Elliptic Curve defined by y^2 = x^3 + ... over Finite Field of size 97] + This can be useful to quickly compute a list of all elliptic curves + over a finite field `k` up to `k`-isomorphism:: + + sage: Es = [E for j in GF(13) for E in EllipticCurve(j=j).twists()] + sage: len(Es) + 32 + sage: Es + [Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of size 13, + ... + Elliptic Curve defined by y^2 = x^3 + ... over Finite Field of size 13] + TESTS: Randomized check that we find all twists and there are no duplicates::