#7331: Conditions for non-split multiplicative reduction in p_primary_bound of
Tate-Shafarevich groups
-------------------------------+--------------------------------------------
Reporter: wuthrich | Owner: davidloeffler
Type: defect | Status: needs_work
Priority: minor | Milestone: sage-4.2.1
Component: elliptic curves | Keywords: sha, tate-shafarevich group,
primary bound
Work_issues: | Author: Christian Wuthrich
Reviewer: Robert Miller | Merged:
-------------------------------+--------------------------------------------
Comment(by rlm):
This one is a different failure:
{{{
sage: E = EllipticCurve('336c')
sage: E.rank()
0
sage: E.is_surjective(3)
(True, None)
sage: E.has_additive_reduction(3)
False
sage: E.has_nonsplit_multiplicative_reduction(3)
False
sage: E.is_good(3)
False
sage: E.is_ordinary(3)
True
sage: E.has_split_multiplicative_reduction(3)
True
sage: E.sha().p_primary_bound(3)
Traceback (most recent call last):
/space/rlm/sage-4.2.alpha0-x86_64-Linux/local/lib/python2.6/site-
packages/sage/schemes/elliptic_curves/sha_tate.pyc in
p_primary_bound(self, p)
588 if not su :
589 raise ValueError, "The mod-p Galois representation
is not surjective. Current knowledge about Euler systems does not provide
an upper bound in this case. Try an_padic for a conjectural bound."
--> 590 shan = self.an_padic(p,prec = 0,use_twists=True)
591 if shan == 0:
592 raise RuntimeError, "There is a bug in an_padic."
/space/rlm/sage-4.2.alpha0-x86_64-Linux/local/lib/python2.6/site-
packages/sage/schemes/elliptic_curves/sha_tate.pyc in an_padic(self, p,
prec, use_twists)
450 not_yet_enough_prec = True
451 while not_yet_enough_prec:
--> 452 lps = lp.series(n,quadratic_twist=D,prec=r+1)
453 lstar = lps[r]
454 if (lstar != 0) or (prec != 0):
/space/rlm/sage-4.2.alpha0-x86_64-Linux/local/lib/python2.6/site-
packages/sage/schemes/elliptic_curves/padic_lseries.pyc in series(self, n,
quadratic_twist, prec)
762 for ell in prime_divisors(D):
763 if valuation(self._E.conductor(),ell) >
valuation(D,ell) :
--> 764 raise ValueError, "can not twist a curve
of conductor (=%s) by the quadratic twist (=%s)."%(self._E.conductor(),D)
765
766
ValueError: can not twist a curve of conductor (=168) by the quadratic
twist (=-4).
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7331#comment:3>
Sage <http://www.sagemath.org>
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