Binary quadratic forms and elliptic curves with analytic rank one

2026/07/21 by Tong Wei, Shuai Zhai
#math.NT

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Abstract

Given an elliptic curve with Weierstrass equation y²=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 dy²=f(x) has analytic rank one.

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