Selmer ranks under quadratic twists satisfying the Heegner hypothesis

Alexandros Konstantinou

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arXiv · 2510.23291

Selmer ranks under quadratic twists satisfying the Heegner hypothesis

Alexandros Konstantinou

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Abstract

We investigate variations of Selmer ranks under quadratic twists satisfying the Heegner hypothesis. In particular, starting with an elliptic curve $E/\mathbb{Q}$ with partial $2$-torsion and a common relaxed Selmer group, we derive explicit formulae describing the effect of twisting on Selmer ranks in terms of matrices over $\mathbb{F}_{2}$. As an application, we show that these formulae are compatible with predictions made by the parity conjecture.

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Alexandros Konstantinou. 2025-10-27. Selmer ranks under quadratic twists satisfying the Heegner hypothesis. https://arxiv.org/abs/2510.23291

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