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Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves.

Abstract:

This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of these conjectures relates six quantities associated to a Jacobian over the rational numbers. One of these six quantities is the size of the Shafarevich-Tate group. Unable to compute that, we computed the five other quantities and solved for the last one. In all 32 cases, the result is very close to an integer that is a power of 2. In addition, this power ...

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Publication status:
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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Leprévost, F More by this author
Schaefer, EF More by this author
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Journal:
Math. Comput.
Volume:
70
Issue:
236
Pages:
1675-1697
Publication date:
2001
DOI:
ISSN:
0025-5718
URN:
uuid:0c6d7e1f-5a0c-432f-85e3-ac20f39a6c62
Source identifiers:
574
Local pid:
pubs:574

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