Dear sage-devel,
I am running into an issue with computing isogeny classes of elliptic
curves over number fields.
Here is what I entered:
K.<a> = QuadraticField(4569)
myJ = 46969655/32768
E = EllipticCurve(j=K(myJ))
C = E.isogeny_class()
This raises a KeyError in the first instance, which seems to be handled via
a direct call to IsogenyClass_EC_NumberField, but this then raises a
ValueError: Cannot convert infinity or NaN to Sage Integer. The full stack
trace is in the PS.
This error has occurred on sage-9.4 on a system whose `uname -a` is `Linux
LEGENDRE 5.4.0-91-generic #102-Ubuntu SMP Fri Nov 5 16:31:28 UTC 2021
x86_64 x86_64 x86_64 GNU/Linux`, as well as on sage-9.7-beta5 on `Linux
Barinder 5.4.0-121-generic #137-Ubuntu SMP Wed Jun 15 13:33:07 UTC 2022
x86_64 x86_64 x86_64 GNU/Linux`.
Changing the field K to many other quadratic fields does not yield any
error. However I did also notice this error with many j-invariants in
QuadraticField(6537), so it somehow seems to be base-field dependent.
Best wishes,
Barinder
PS. Full traceback:
---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/structure/category_object.pyx
in sage.structure.category_object.CategoryObject.getattr_from_category
(build/cythonized/sage/structure/category_object.c:7074)()
838 try:
--> 839 return self.__cached_methods[name]
840 except KeyError:
KeyError: '_isoclass'
During handling of the above exception, another exception occurred:
AttributeError Traceback (most recent call last)
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_number_field.py
in isogeny_class(self, reducible_primes, algorithm, minimal_models)
3007 try:
-> 3008 return self._isoclass
3009 except AttributeError:
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/structure/category_object.pyx
in sage.structure.category_object.CategoryObject.__getattr__
(build/cythonized/sage/structure/category_object.c:6993)()
832 """
--> 833 return self.getattr_from_category(name)
834
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/structure/category_object.pyx
in sage.structure.category_object.CategoryObject.getattr_from_category
(build/cythonized/sage/structure/category_object.c:7159)()
847
--> 848 attr = getattr_from_other_class(self, cls, name)
849 self.__cached_methods[name] = attr
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/cpython/getattr.pyx
in sage.cpython.getattr.getattr_from_other_class
(build/cythonized/sage/cpython/getattr.c:2552)()
366 dummy_error_message.name = name
--> 367 raise AttributeError(dummy_error_message)
368 cdef PyObject* attr = instance_getattr(cls, name)
AttributeError: 'sage.sets.pythonclass.Set_PythonType_class' object has no
attribute '_Hom_'
During handling of the above exception, another exception occurred:
ValueError Traceback (most recent call last)
<ipython-input-1-a9c20a51d066> in <module>
2 myJ = Integer(46969655)/Integer(32768)
3 E = EllipticCurve(j=K(myJ))
----> 4 C = E.isogeny_class()
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_number_field.py
in isogeny_class(self, reducible_primes, algorithm, minimal_models)
3009 except AttributeError:
3010 from sage.schemes.elliptic_curves.isogeny_class import
IsogenyClass_EC_NumberField
-> 3011 self._isoclass = IsogenyClass_EC_NumberField(self,
reducible_primes=reducible_primes, algorithm=algorithm,
minimal_models=minimal_models)
3012 return self._isoclass
3013
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/isogeny_class.py
in __init__(self, E, reducible_primes, algorithm, minimal_models)
705 self._algorithm = algorithm
706 self._minimal_models = minimal_models
--> 707 IsogenyClass_EC.__init__(self, E, label=None, empty=False)
708
709 def copy(self):
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/isogeny_class.py
in __init__(self, E, label, empty)
68 self._label = label
69 if not empty:
---> 70 self._compute()
71
72 def __len__(self):
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/isogeny_class.py
in _compute(self, verbose)
789 sys.stdout.write(" possible isogeny degrees: %s" % degs)
790 sys.stdout.flush()
--> 791 isogenies = E.isogenies_prime_degree(degs,
minimal_models=self._minimal_models)
792 if verbose:
793 sys.stdout.write(" -actual isogeny degrees: %s" %
Set(phi.degree() for phi in isogenies))
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_number_field.py
in isogenies_prime_degree(self, l, algorithm, minimal_models)
3108 return self.isogenies_prime_degree(L,
minimal_models=minimal_models)
3109
-> 3110 isogs = sum([self.isogenies_prime_degree(p,
minimal_models=minimal_models) for p in l],
3111 [])
3112
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_number_field.py
in <listcomp>(.0)
3108 return self.isogenies_prime_degree(L,
minimal_models=minimal_models)
3109
-> 3110 isogs = sum([self.isogenies_prime_degree(p,
minimal_models=minimal_models) for p in l],
3111 [])
3112
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_number_field.py
in isogenies_prime_degree(self, l, algorithm, minimal_models)
3097 try:
3098 if l.is_prime(proof=False):
-> 3099 return isogenies_prime_degree(self, l,
minimal_models=minimal_models)
3100 else:
3101 raise ValueError("%s is not prime." % l)
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/isogeny_small_degree.py
in isogenies_prime_degree(E, l, minimal_models)
2340 return isogenies_2(E, minimal_models=minimal_models)
2341 if l==3:
-> 2342 return isogenies_3(E, minimal_models=minimal_models)
2343
2344 p = E.base_ring().characteristic()
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/isogeny_small_degree.py
in isogenies_3(E, minimal_models)
754 from sage.rings.number_field.number_field_base import
is_NumberField
755 model = "minimal" if minimal_models and
is_NumberField(E.base_field()) else None
--> 756 isogs = [E.isogeny(f, model=model) for f in ff]
757 return isogs
758
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/isogeny_small_degree.py
in <listcomp>(.0)
754 from sage.rings.number_field.number_field_base import
is_NumberField
755 model = "minimal" if minimal_models and
is_NumberField(E.base_field()) else None
--> 756 isogs = [E.isogeny(f, model=model) for f in ff]
757 return isogs
758
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_field.py
in isogeny(self, kernel, codomain, degree, model, check)
876 """
877 try:
--> 878 return EllipticCurveIsogeny(self, kernel, codomain,
degree, model, check=check)
879 except AttributeError as e:
880 raise RuntimeError("Unable to construct isogeny: %s" %
e)
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py
in __init__(self, E, kernel, codomain, degree, model, check)
1015 self.__compute_E2()
1016
-> 1017 self.__setup_post_isomorphism(codomain, model)
1018
1019 if (pre_isom is not None):
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py
in __setup_post_isomorphism(self, codomain, model)
1800 raise ValueError("specifying minimal for model
flag only valid with curves over number fields.")
1801
-> 1802 newE2 = oldE2.global_minimal_model(semi_global=True)
1803 post_isom = oldE2.isomorphism_to(newE2)
1804
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_number_field.py
in global_minimal_model(self, proof, semi_global)
2042 from .kraus import semi_global_minimal_model
2043 E, P = semi_global_minimal_model(self)
-> 2044 return E._scale_by_units()._reduce_model()
2045
2046 raise ValueError("%s has no global minimal model! For a
semi-global minimal model use semi_global=True" % self)
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_number_field.py
in _scale_by_units(self)
987 from sage.modules.all import vector
988 v =
vector([(x4.abs().nth_root(4)+x6.abs().nth_root(6)).log()*d for x4,x6,d in
zip(c4s,c6s,degs)])
--> 989 es = [e.round() for e in -Ainv*U*v]
990 u = prod([uj**ej for uj,ej in zip(fu,es)])
991 return self.scale_curve(u)
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/schemes/elliptic_curves/ell_number_field.py
in <listcomp>(.0)
987 from sage.modules.all import vector
988 v =
vector([(x4.abs().nth_root(4)+x6.abs().nth_root(6)).log()*d for x4,x6,d in
zip(c4s,c6s,degs)])
--> 989 es = [e.round() for e in -Ainv*U*v]
990 u = prod([uj**ej for uj,ej in zip(fu,es)])
991 return self.scale_curve(u)
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/rings/real_mpfr.pyx
in sage.rings.real_mpfr.RealNumber.round
(build/cythonized/sage/rings/real_mpfr.c:22391)()
3015 cdef RealNumber x = self._new()
3016 mpfr_round(x.value, self.value)
-> 3017 return x.integer_part()
3018
3019 def floor(self):
/scratch/sage/sage-9.4/local/lib/python3.8/site-packages/sage/rings/real_mpfr.pyx
in sage.rings.real_mpfr.RealNumber.integer_part
(build/cythonized/sage/rings/real_mpfr.c:17420)()
2256 """
2257 if not mpfr_number_p(self.value):
-> 2258 raise ValueError('Cannot convert infinity or NaN to
Sage Integer')
2259
2260 cdef Integer z = Integer()
ValueError: Cannot convert infinity or NaN to Sage Integer
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