Selmer ranks under quadratic twists satisfying the Heegner hypothesis
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909871013625856 |
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| author | Konstantinou, Alexandros |
| author_facet | Konstantinou, Alexandros |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23291 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Selmer ranks under quadratic twists satisfying the Heegner hypothesis Konstantinou, Alexandros Number Theory 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. |
| title | Selmer ranks under quadratic twists satisfying the Heegner hypothesis |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.23291 |