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March 2017 Elliptic curves with rank $0$ over number fields
Pallab Kanti Dey
Funct. Approx. Comment. Math. 56(1): 25-37 (March 2017). DOI: 10.7169/facm/1585

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 $K$.

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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

Information

Published: March 2017
First available in Project Euclid: 19 January 2017

zbMATH: 06864143
MathSciNet: MR3629008
Digital Object Identifier: 10.7169/facm/1585

Subjects:
Primary: 14H52
Secondary: 11R04

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.56 • No. 1 • March 2017
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