Abstract
Let $E: y^2 = x^3 + bx$ be an elliptic curve for some nonzero integer $b$. Also consider $K$ be a number field with $4 \nmid [K : \mathbb{Q}]$. Then in this paper, we obtain a necessary and sufficient condition for $E$ having rank $0$ over $K$.
Citation
Pallab Kanti Dey. "Elliptic curves with rank $0$ over number fields." Funct. Approx. Comment. Math. 56 (1) 25 - 37, March 2017. https://doi.org/10.7169/facm/1585
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