## Experimental Mathematics

- Experiment. Math.
- Volume 9, Issue 4 (2000), 583-590.

### Ranks of elliptic curves in families of quadratic twists

Karl Rubin and Alice Silverberg

#### Abstract

We show that the unboundedness of the ranks of the quadratic twists of an elliptic curve is equivalent to the divergence of certain infinite series.

#### Article information

**Source**

Experiment. Math., Volume 9, Issue 4 (2000), 583-590.

**Dates**

First available in Project Euclid: 20 February 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1045759523

**Mathematical Reviews number (MathSciNet)**

MR1806293

**Zentralblatt MATH identifier**

0959.11023

**Subjects**

Primary: 11G05: Elliptic curves over global fields [See also 14H52]

#### Citation

Rubin, Karl; Silverberg, Alice. Ranks of elliptic curves in families of quadratic twists. Experiment. Math. 9 (2000), no. 4, 583--590. https://projecteuclid.org/euclid.em/1045759523