#18662: Implement (semi-)global minimal models for elliptic curves over number
fields with h>1
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Reporter: cremona | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: elliptic curves | Resolution:
Keywords: Weierstrass | Merged in:
models | Reviewers:
Authors: John Cremona | Work issues:
Report Upstream: N/A | Commit:
Branch: | b7e3b61cf46a9664588ecf7574bff6bde16b01f4
u/cremona/ticket/18662 | Stopgaps:
Dependencies: |
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Changes (by cremona):
* status: new => needs_review
Comment:
Notes for reviewers: The first two commits add small functionality for
number fields (solving CRT systems modulo pairwise coprime ideal lists)
and class groups (get a prime representing any ideal class). The first
could be extended to the non-pairwise coprime case, with suitable error
being raised if there is no solution, but I did not need that.
The main commit is the third one which adds a new file kraus.py,
implementing just about everything in the Kraus paper cited there: see the
docstring at the top of that file for details. The new functionality for
elliptic curves over number fields is achieved by adding some methods, and
enhancing the existing method global_minimal_model() in
ell_number_field.py.
The examples used in the doctests are taken from the LMFDB. The code here
has been run on around a hundred thousand curves over real quadratic
fields (during which time bugs were found and fixed). Not many higher
degree fields have been tested.
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Ticket URL: <http://trac.sagemath.org/ticket/18662#comment:3>
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