## Functiones et Approximatio Commentarii Mathematici

### Elliptic curves with rank $0$ over number fields

Pallab Kanti Dey

#### 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 $K$.

#### Article information

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

Dates
First available in Project Euclid: 19 January 2017

https://projecteuclid.org/euclid.facm/1484794815

Digital Object Identifier
doi:10.7169/facm/1585

Mathematical Reviews number (MathSciNet)
MR3629008

Zentralblatt MATH identifier
06864143

#### Citation

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. https://projecteuclid.org/euclid.facm/1484794815

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