Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves
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 gr...
| المؤلفون الرئيسيون: | , , , , , |
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| التنسيق: | Journal article |
| منشور في: |
2001
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| _version_ | 1826301340437970944 |
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| author | Flynn, E Leprévost, F Schaefer, E Stein, W Stoll, M Wetherell, J |
| author_facet | Flynn, E Leprévost, F Schaefer, E Stein, W Stoll, M Wetherell, J |
| author_sort | Flynn, E |
| collection | OXFORD |
| description | 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 of 2 agrees with the size of the 2-torsion of the Shafarevich-Tate group, which we could compute. |
| first_indexed | 2024-03-07T05:30:56Z |
| format | Journal article |
| id | oxford-uuid:e23f4731-cd7f-4e6b-807d-65e7fc6a982b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:30:56Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:e23f4731-cd7f-4e6b-807d-65e7fc6a982b2022-03-27T09:59:47ZEmpirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e23f4731-cd7f-4e6b-807d-65e7fc6a982bMathematical Institute - ePrints2001Flynn, ELeprévost, FSchaefer, EStein, WStoll, MWetherell, JThis 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 of 2 agrees with the size of the 2-torsion of the Shafarevich-Tate group, which we could compute. |
| spellingShingle | Flynn, E Leprévost, F Schaefer, E Stein, W Stoll, M Wetherell, J Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves |
| title | Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves |
| title_full | Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves |
| title_fullStr | Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves |
| title_full_unstemmed | Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves |
| title_short | Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves |
| title_sort | empirical evidence for the birch and swinnerton dyer conjectures for modular jacobians of genus 2 curves |
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