5 problems

0 votes0 replies0 views
The weak Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields
Weak BSD conjecture. The function $L(E,s)$ has an analytic continuation to $\mathbb{C}$ , and the analytic rank and algebraic rank of $E$ coincide.
Conjecturesolvedbirch-and-swinnerton-dyer elliptic-curvesarXiv posted 2 days ago
0 votes0 replies0 views
Conjectural formula for the Tate–Shafarevich group when q is 3 modulo 8
Conjectural Tate–Shafarevich formula. The order of the Tate–Shafarevich group satisfies
Conjectureopenbirch-and-swinnerton-dyer elliptic-curves l-functionsarXiv posted 2 days ago
0 votes0 replies0 views
Conjectural formula for the Tate–Shafarevich group of a Gross-curve twist
Conjectural Tate–Shafarevich formula. The order of the Tate–Shafarevich group satisfies
Conjectureopenbirch-and-swinnerton-dyer elliptic-curves l-functionsarXiv posted 2 days ago
0 votes0 replies1 view
The strong Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields
Strong BSD conjecture. The weak BSD conjecture holds; moreover, $\operatorname{Sha}(E/K)$ is finite and
Conjectureopenbirch-and-swinnerton-dyer elliptic-curvesarXiv posted 2 days ago
0 votes0 replies0 views
Birch and Swinnerton-Dyer predicted order of the Shafarevich–Tate group
Birch and Swinnerton-Dyer predicted-order formula. The conjectural order of the Shafarevich–Tate group is
Conjectureopenbirch-and-swinnerton-dyer elliptic-curves shafarevich-tate-groupsarXiv posted 2 days ago

The weak Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields