On the Jacobian of hyperelliptic curves $y^2=x^5+m^2$

Keunyoung Jeong, Junyeong Park, Donggeon Yhee

In this paper, we study the algebraic rank and the analytic rank of the Jacobian of hyperelliptic curves $y^2=x^5+m^2$ for integers $m$. Namely, we first provide a condition on…