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arXiv · 1805.05862

The Birch and Swinnerton-Dyer conjecture for an elliptic curve over $\mathbb{Q}(\sqrt[4]{5})$

Raymond van Bommel
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Abstract

In this paper we show the Birch and Swinnerton-Dyer conjecture for a certain elliptic curve over $\mathbb{Q}(\sqrt[4]{5})$ is equivalent to the same conjecture for a certain pair of hyperelliptic curves of genus 2 over $\mathbb{Q}$. We numerically verify the conjecture for these hyperelliptic curves. Moreover, we explain the methods used to find this example, which turned out to be a bit more subtle than expected.

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Raymond van Bommel. 2018-05-15. The Birch and Swinnerton-Dyer conjecture for an elliptic curve over $\mathbb{Q}(\sqrt[4]{5})$. https://arxiv.org/abs/1805.05862

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