Elliptic curves with CM over number fields fail to find all isogenies

[JohnCremona]

Steps To Reproduce

Define an elliptic curve E over a real quadratic number field, where j(E) = 0, compute E.isogeny_class(), and look at the degrees it finds. Example:
sage: L5. = NumberField(x^2-5)
sage: F = EllipticCurve(L5,[0,-4325477943600*r5-4195572876000])
sage: F.isogeny_class().matrix()
[1 3]
[3 1]

Expected Behavior

The matrix should include isogenies of degree 5 (and more).

Actual Behavior

It only find 3-isogenies (see above).

Additional Information

As reported to sage-support: https://groups.google.com/g/sage-support/c/1BfJIGIlb0M

The problem is in the function sage.schemes.elliptic_curves.isogeny_class.isogeny_degrees.cm, where the degree bound called n there needs to be multiplied by 3 for j=0, d=-3 (and by 2 for j=1728, d=-4).

A PR is in preparation. Only curves with j=0 or j=1728 are affected (and not all these).

Environment

- **OS**: any
- **Sage Version**: 10.2rc3

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[JohnCremona]

The curve is defined by
sage: K. = NumberField(x^2-5)
sage: t = -4320 - 1944r
sage: E = EllipticCurve([0, -27t^2, 0, 216t^3(t - 27), -432t^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.

[JohnCremona]

Sorry for the noise: I was testing on an old Sage, there is no problem now (10.4.beta4).