Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves
نویسندگان
چکیده
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 ShafarevichTate 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.
منابع مشابه
Collected Works
This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of theseconjectures relates six quantities associated to a Jacobian over the rationalnumbers. 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...
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ورودعنوان ژورنال:
- Math. Comput.
دوره 70 شماره
صفحات -
تاریخ انتشار 2001