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. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAD0p0K5qJt_u1hHsJBS%2Boukk6yJfwF6R-OyB5eRsQzWBxgSjhQ%40mail.gmail.com.