Asuka Shiga

collaborators

3 papers

math.NT2026

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants

Asuka Shiga

Let $E/\mathbb{Q}$ be an elliptic curve. The Birch and Swinnerton--Dyer (BSD) conjecture relates the leading coefficient of the Taylor expansion of the $L$-function of \(E/\mat…

math.NT2026

Nontrivial torsion in the Tate--Shafarevich group of elliptic curves via visibility and twists

Asuka Shiga

Let $ℓ$ be an odd prime. We study the visibility theorem for certain elliptic curves over $Q$ with additive reduction at $ℓ$ , and deduce the existence of nontrivial…

math.NT2025

Behaviors of the Tate--Shafarevich group of elliptic curves under quadratic field extensions

Asuka Shiga

Let $E / Q$ be an elliptic curve. We study the behavior of the Tate--Shafarevich group of $E$ under quadratic extensions $Q (D) / Q$ . By analyzing the…