bug in documentation for non_surjective for Galois representations attached to elliptic curves

[sagetrac-dpathakjee]

non_surjective() docstring incorrectly states that it's inconclusive and often wrong for p=2. The function it calls, is_surjective, is correct for p=2.

The docstring states that "[the] list of primes p such that the mod-p representation might not be surjective... usually contains 2, because of shortcomings of the algorithm..." However, non_surjective calls is_surjective, which should always be correct for p=2,3 because it computes the Galois group of the 2-division polynomial. (More precisely, its helper, _is_surjective, does this.) I suspect this caveat may have been written before the special cases for p=2,3 in _is_surjective had been written.

All that really needs to be done is to remove the phrase "(this list usually contains 2, because of shortcomings of the algorithm)" from the docstring.

See also #11271, #11270

CC: @williamstein

Component: elliptic curves

Keywords: galois representation, non_surjective

Reviewer: Chris Wuthrich

Issue created by migration from https://trac.sagemath.org/ticket/11276

[chriswuthrich]

comment:3

This is a duplicate (well, striclty speaking a sub-ticket) of #11271. This should be closed.

[pjbruin]

Reviewer: Chris Wuthrich