#16773: Analytic Rank Bound
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Reporter: spice | Owner: spice
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: elliptic curves | Resolution:
Keywords: elliptic curves, | Merged in:
analytic rank, l-functions | Reviewers: William Stein
Authors: Simon Spicer | Work issues:
Report Upstream: N/A | Commit:
Branch: | 7b4f9d849cf14e709e90880dbdbd5b51b3524b62
u/spice/analytic_rank_bound | Stopgaps:
Dependencies: |
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Description changed by spice:
Old description:
> Implement functionality to bound from above the analytic rank of a
> rational elliptic curve. This uses the zero sum method as described in
> [http://msp.org/obs/2013/1-1/obs-v1-n1-p07-s.pdf]. Because this avoids
> computing with the curve's L-function directly, it is often faster than
> traditional analytic rank techniques.
>
> The enhancement also includes functionality to compute more general zero
> sums for an elliptic curve L-function, as well as computing with the
> logarithmic derivative.
New description:
Implement functionality to bound from above the analytic rank of a
rational elliptic curve. This uses the zero sum method as described in
[http://msp.org/obs/2013/1-1/obs-v1-n1-p07-s.pdf]. Because this avoids
computing with the curve's L-function directly, it is often faster than
traditional analytic rank techniques.
The enhancement also includes functionality to compute more general zero
sums for an elliptic curve L-function, as well as computing with the
logarithmic derivative. The elliptic_curves object in Sage has also been
modified to contain examples of elliptic curves up to rank 28. To this end
the elliptic_curves spkg has been updated to version 0.8. The archived
data file can be obtained at
[https://cloud.sagemath.com/projects/8499bab7-d4a5-4956-acd2-248b5550731d/files/elliptic_curves-0.8.tar.bz2]
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Ticket URL: <http://trac.sagemath.org/ticket/16773#comment:12>
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