#16456: Bug in descend_to method for elliptic curves
-------------------------------------+-------------------------------------
Reporter: cremona | Owner: cremona
Type: defect | Status: needs_work
Priority: major | Milestone: sage-6.3
Component: elliptic curves | Resolution:
Keywords: elliptic curve | Merged in:
base change | Reviewers: Peter Bruin
Authors: John Cremona | Work issues:
Report Upstream: N/A | Commit:
Branch: | e6ccee27c60c15aac6f103a0b5303450e36789c1
u/cremona/16456-descend_to_bug | Stopgaps:
Dependencies: #16708 |
-------------------------------------+-------------------------------------
Changes (by pbruin):
* status: needs_review => needs_work
Comment:
Replying to [comment:18 cremona]:
> Between here and #16708 a doctest needed changing as I think Peter
pointed out somewhere:
> {{{
> sage: K.<a> = QuadraticField(-5)
> sage: list(K.selmer_group_iterator((), 4))
> [1, 2, 4, 8, -1, -2, -4, -8]
> }}}
> should be
> {{{
> sage: K.<a> = QuadraticField(-5)
> sage: list(K.selmer_group_iterator((), 4))
> [1, 4, 16, 64, -1, -4, -16, -64]
> }}}
> which I am changing and will commit & push.
That second answer was actually the wrong "correction" I pushed and then
retracted. It should be `[1, 4, -1, -4]` (as in comment:17); in fact 16
is a fourth power, hence represents the trivial element of the Selmer
group. The Selmer group is isomorphic to ''C'',,2,, x ''C'',,2,, (since
both the units modulo 4-th powers and the 4-torsion in the class group are
cyclic of order 2.)
I think the problem is the line
{{{
f = lambda o: m if o is Infinity else o.gcd(m)
}}}
where you will somehow need to take the orders of elements of the class
group into account.
--
Ticket URL: <http://trac.sagemath.org/ticket/16456#comment:21>
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