#5307: Bug in conductor() over number fields
---------------------------+------------------------------------------------
Reporter: cremona | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.4
Component: number theory | Keywords: elliptic curve
---------------------------+------------------------------------------------
There is something wrong in the conductor computation of an elliptic curve
over a field of class number >1:
{{{
sage: K.<w>=NumberField(x^2+x+6)
sage: E=EllipticCurve([w,-1,0,-w-6,0])
sage: E.conductor()
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/masgaj/.sage/temp/host_56_150/7547/_home_masgaj__sage_init_sage_0.py
in <module>()
/local/jec/sage-3.3.rc0/local/lib/python2.5/site-
packages/sage/schemes/elliptic_curves/ell_number_field.pyc in
conductor(self)
745 OK = self.base_ring().ring_of_integers()
746 self._conductor =
prod([d.prime()**(d.conductor_valuation()) \
--> 747 for d in self.local_data()],\
748 OK.ideal(1))
749 return self._conductor
/local/jec/sage-3.3.rc0/local/lib/python2.5/site-
packages/sage/schemes/elliptic_curves/ell_number_field.pyc in
local_data(self, P, proof)
394 if P is None:
395 primes =
self.base_ring()(self.discriminant()).support()
--> 396 return [self._get_local_data(pr, proof) for pr in
primes]
397
398 from sage.schemes.elliptic_curves.ell_local_data import
check_prime
/local/jec/sage-3.3.rc0/local/lib/python2.5/site-
packages/sage/schemes/elliptic_curves/ell_number_field.pyc in
_get_local_data(self, P, proof)
416 pass
417 from sage.schemes.elliptic_curves.ell_local_data import
EllipticCurveLocalData
--> 418 self._local_data[P] = EllipticCurveLocalData(self, P,
proof)
419 return self._local_data[P]
420
/local/jec/sage-3.3.rc0/local/lib/python2.5/site-
packages/sage/schemes/elliptic_curves/ell_local_data.pyc in __init__(self,
E, P, proof, algorithm)
138 self._reduction_type = Eint.ap(p) # = 0,-1 or +1
139 else:
--> 140 self._Emin, ch, self._val_disc, self._fp, self._KS,
self._cp, self._split = self._tate(proof)
141 if self._fp>0:
142 if self._Emin.c4().valuation(p)>0:
/local/jec/sage-3.3.rc0/local/lib/python2.5/site-
packages/sage/schemes/elliptic_curves/ell_local_data.pyc in _tate(self,
proof)
748 a6 /= pi**6
749 verbose("Non-minimal equation, dividing
out...\nNew model is %s"%([a1, a2, a3, a4, a6]), t, 1)
--> 750 C = C._tidy_model()
751 return (C, p, val_disc, fp, KS, cp, split)
752
/local/jec/sage-3.3.rc0/local/lib/python2.5/site-
packages/sage/schemes/elliptic_curves/ell_number_field.pyc in
_tidy_model(self)
297 (a1, a2, a3, a4, a6) = [ZK(a) for a in
self.a_invariants()]
298 except TypeError:
--> 299 raise TypeError, "_tidy_model() requires an integral
model."
300 # N.B. Must define s, r, t in the right order.
301 if ZK.degree() == 1:
TypeError: _tidy_model() requires an integral model.
}}}
I think I wrote most of the relevant code, so it is my fault and I will
fix it!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5307>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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