False alarm -- the current version of Safe computes this correctly, presumably because of the bugfix I made.
So this is no longer a Sage issue, but the LMFDB will need to be corrected. John On Wed, 1 May 2024 at 08:51, John Cremona <john.crem...@gmail.com> wrote: > This looks like the same bug as I reported at > https://github.com/sagemath/sage/issues/36780 five months ago and > supposedly fixed via a PR (https://github.com/sagemath/sage/pull/36786). > It's the same bug (over Q(sqrt(5)), j=0, missing a 5-isogeny) so clearly my > fix was incorrect. > > The curve is defined by > sage: K.<r> = NumberField(x^2-5) > sage: t = -4320 - 1944*r > sage: E = EllipticCurve([0, -27*t^2, 0, 216*t^3*(t - 27), -432*t^4*(t - > 27)^2]) > sage: E.has_cm() > True > sage: E.cm_discriminant() > -75 > sage: C = E.isogeny_class() > sage: len(C) > 6 > sage: C.matrix()[0] > (1, 25, 75, 3, 5, 15) > > This is all correct, the class has size 6 and 3- and 5- isogenies suffice > to fill it. But the class contains two curves defined over Q for example > sage: E1 = C[5]; E1.ainvs() > (0, 0, 1, 0, 1) > sage: E1.j_invariant() > 0 > sage: E1.base_field() == K > True > > and computing the isogeny class starting with E1 does not find the whole > class as it misses 5-isogenies: > > sage: len(E1.isogeny_class()) > 2 > > The problem is in the function possible_isogeny_degrees_cm(): > sage: from sage.schemes.elliptic_curves.isogeny_class import > isogeny_degrees_cm > sage: isogeny_degrees_cm(E1, verbose=True) > CM case, discriminant = -3 > initial primes: {2, 3} > ramified primes: {3} > downward split primes: {} > downward inert primes: {} > Complete set of primes: {2, 3} > [2, 3] > > Here, "downward" primes are sgrees of isogenies to curves with a strictly > smaller endomorphism ring and in this case should inlude 5. I cannot right > now see the error in the code but am building the current development > branch and will sort this out. > > John > > On Tue, 30 Apr 2024 at 17:08, John Cremona <john.crem...@gmail.com> wrote: > >> I can confirm that your curve is isogenous (and not isomorphic) to the >> ones in the LMFDB. The isogeny class computed by Sage from your curve has >> 6 curves in it. That means that there is a bug in Sage's isogeny class >> code -- which I wrote most of. I hope that it is something specific to >> j-invariant 0, which is (as always) treated separately. >> >> I will investigate the Sage bug, and when it is fixed I will recompute >> all the isogeny classes in the LMFDB. This will not be done very soon. >> >> Thanks for the report! >> >> John >> >> On Tue, 30 Apr 2024 at 16:42, Zhengyu Tao <tao...@smail.nju.edu.cn> >> wrote: >> >>> Thanks for your reply! The coefficients of my curve is [0, -27*t^2, 0, >>> 216*t^3*(t - 27), -432*t^4*(t - 27)^2] with t = -4320 - 1944\sqrt{5}. >>> >>> ------------------ Original ------------------ >>> *From: * "John Cremona"<john.crem...@gmail.com>; >>> *Date: * Tue, Apr 30, 2024 11:35 PM >>> *To: * "John Jones"<j...@asu.edu>; >>> *Cc: * "lmfdb-support"<lmfdb-supp...@googlegroups.com>; "taozhy"< >>> tao...@smail.nju.edu.cn>; >>> *Subject: * Re: EC question >>> >>> The isogeny classes in the LMFDB are supposed to be complete. I see >>> that curve 2.2.5.1-2025.1-d2 has coefficients (0, 0, 1, 0, -34) while the >>> isogenous curve d1 has coefficients (0, 0, 1, 0, 1), both with j-invariant >>> 0 and conductor (45) over this field. They are quadratic twists of each >>> other by -3. >>> >>> What are the coefficients of the curve you have? If it is not >>> isomorphic to either of these then there is a bug in Sage, which was used >>> to compute the isogeny classes. >>> >>> John Cremona >>> >>> On Tue, 30 Apr 2024 at 16:08, John Jones <j...@asu.edu> wrote: >>> >>>> From the feedback page: >>>> >>>> Hi LMFDB devs, >>>> >>>> In a recent problem I'm working on, I need to compute a (CM) elliptic >>>> curve over Q(\sqrt{5}). When I searched it in LMFDB, it seems that it is >>>> not included. However, I found that my curve seems isogenous (over >>>> Q(\sqrt{5})) to the curve 2.2.5.1-2025.1-d2. In fact, I have constructed >>>> the isogeny from my curve to 2.2.5.1-2025.1-d2 using velu'formula. >>>> >>>> My qusetion is: is the isogeny classes in LMFDB complete? I.e., is each >>>> isomorphism class (over the base field) in a isogeny class has a >>>> representative in LMFDB's "isogeny class"? >>>> >>>> Best regards, >>>> Zhengyu Tao >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "lmfdb-support" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to lmfdb-support+unsubscr...@googlegroups.com. >>>> To view this discussion on the web, visit >>>> https://groups.google.com/d/msgid/lmfdb-support/CAJciYuQy0AS%3D29ceGLXnAxgMt5Z_01VQj5nom5WHU4kH%3Djf6uA%40mail.gmail.com >>>> <https://groups.google.com/d/msgid/lmfdb-support/CAJciYuQy0AS%3D29ceGLXnAxgMt5Z_01VQj5nom5WHU4kH%3Djf6uA%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>> . >>>> >>> -- You received this message because you are subscribed to the Google Groups "sage-support" group. 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