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• W1534446261 abstract "This paper investigates which integers can appear as 2-Selmer ranks within the quadratic twist family of an elliptic curve E defined over a number field K with E(K)[2] = Z/2Z. We show that if E does not have a cyclic 4-isogeny defined over K(E[2]), then subject only to constant 2-Selmer parity, each non-negative integer appears infinitely often as the 2-Selmer rank of a quadratic twist of E. If E has a cyclic 4-isogeny defined over K(E[2]) but not over K, then we prove the same result for 2-Selmer ranks greater than or equal to r_2, the number of complex places of K. We also obtain results about the minimum number of twists of E with rank 0, and subject to standard conjectures, the number of twists with rank 1, provided E does not have a cyclic 4-isogeny defined over K." @default.
• W1534446261 created "2016-06-24" @default.
• W1534446261 creator A5050799117 @default.
• W1534446261 date "2016-10-12" @default.
• W1534446261 modified "2023-09-26" @default.
• W1534446261 title "Selmer ranks of quadratic twists of elliptic curves with partial rational two-torsion" @default.
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• W1534446261 doi "https://doi.org/10.1090/tran/6744" @default.
• W1534446261 hasPublicationYear "2016" @default.
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