#8238: heegner_index_bound may be incorrect for curves with rational torsion
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Reporter: rlm | Owner: cremona
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.4
Component: elliptic curves | Keywords:
Author: Robert Miller | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by was):
* status: needs_review => needs_work
* milestone: => sage-4.4
Comment:
Robert,
I think the point of this patch is to change the function so it is no
longer off by factors of 2 by default.
Note that the documentation, even after applying your patch, says:
{{{
r"""
Return an interval that contains the index of the Heegner
point `y_K` in the group of `K`-rational points modulo torsion
on this elliptic curve, computed using the Gross-Zagier
formula and/or a point search, or the index divided by `2`.
.. note::
If ``min_p`` is bigger than 2 then the index can be off by
any prime less than ``min_p``. This function returns the
index divided by `2` exactly when the rank of `E(K)` is
greater than 1 and `E(\QQ)_{/tor} \oplus E^D(\QQ)_{/tor}`
has index `2` in `E(K)_{/tor}`, where the second factor
undergoes a twist.
}}}
If you've really fixed the "factor of 2" issue, as it seems you have, then
the documentation should be changed to reflect this. Moreover, this is an
enhancement, rather than a bug fix.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8238#comment:4>
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