Binary quadratic forms and elliptic curves with analytic rank one

Tong Wei; Shuai Zhai

Binary quadratic forms and elliptic curves with analytic rank one

Number Theory 2026-07-21 v1

Authors: Tong Wei , Shuai Zhai

Abstract

Given an elliptic curve with Weierstrass equation $y^2=f(x)$ , and a positive definite binary quadratic form $Q(u, v)$ . We show that there are infinitely many $d$ in the set represented by the quadratic forms in the genus of $Q$ such that the twisted elliptic curve $dy^2=f(x)$ has analytic rank one.

Cite

@article{arxiv.2607.18728,
  title  = {Binary quadratic forms and elliptic curves with analytic rank one},
  author = {Tong Wei and Shuai Zhai},
  journal= {arXiv preprint arXiv:2607.18728},
  year   = {2026}
}

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13 pages