Open Access
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


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 $K$.


Download Citation

Pallab Kanti Dey. "Elliptic curves with rank $0$ over number fields." Funct. Approx. Comment. Math. 56 (1) 25 - 37, March 2017.


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

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

Primary: 14H52
Secondary: 11R04

Keywords: Diophantine equation , Elliptic curve , number field

Rights: Copyright © 2017 Adam Mickiewicz University

Vol.56 • No. 1 • March 2017
Back to Top