In this paper we consider the question of when all Seshadri constants on a product of two isogenous elliptic curves \(E_1\times E_2\) without complex multiplication are integers. By studying elliptic curves on \(E_1\times E_2\) we translate this question into a purely numerical problem expressed by quadratic forms. By solving that problem, we show that all Seshadri constants on \(E_1\times E_2\) are integers if and only if the minimal degree of an isogeny \(E_1\rightarrow E_2\) equals 1 or 2. Furthermore, this method enables a characterization of irreducible principal polarizations on \(E_1\times E_2\).

在本文中，我们考虑以下问题：两个无复数乘法的同构椭圆曲线\（E_1 \ times E_2 \）的乘积上的所有Seshadri常数何时都是整数。通过研究\（E_1 \ times E_2 \）上的椭圆曲线，我们将此问题转换为由二次形式表示的纯数值问题。通过解决该问题，我们证明，当且仅当同构子的最小程度\（E_1 \ rightarrow E_2 \）等于1或2时，\（E_1 \ times E_2 \）上的所有Seshadri常数都是整数。\（E_1 \ times E_2 \）上不可归约的主极化的刻画。