Functiones et Approximatio Commentarii Mathematici

Elliptic curves with rank $0$ over number fields

Pallab Kanti Dey

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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 $K$.

Article information

Funct. Approx. Comment. Math., Volume 56, Number 1 (2017), 25-37.

First available in Project Euclid: 19 January 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx]
Secondary: 11R04: Algebraic numbers; rings of algebraic integers

elliptic curve number field Diophantine equation


Dey, Pallab Kanti. Elliptic curves with rank $0$ over number fields. Funct. Approx. Comment. Math. 56 (2017), no. 1, 25--37. doi:10.7169/facm/1585.

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