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Quadratic twist families of elliptic curves with unusual $2^{\infty }$-Selmer groups

By Alexander Smith

Appears in collection : Jean-Morlet Chair - Conference - Arithmetic Statistics / Chaire Jean-Morlet - Conférence - Statistiques arithmétiques

Given any elliptic curve $E$ over the rationals, we show that 50 % of the quadratic twists of $E$ have $2^{\infty}$-Selmer corank 0 and 50 % have $2^{\infty}$-Selmer corank 1. As a result, we show that Goldfeld's conjecture follows from the Birch and Swinnerton-Dyer conjecture.

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Citation data

  • DOI 10.24350/CIRM.V.20046203
  • Cite this video Smith, Alexander (16/05/2023). Quadratic twist families of elliptic curves with unusual $2^{\infty }$-Selmer groups. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20046203
  • URL https://dx.doi.org/10.24350/CIRM.V.20046203


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