Parity of ranks of elliptic curves with equivalent mod p Galois representations - Shekhar, Sudhanshu (Proceedings of the American Mathematical Society, 2016)
Given two elliptic curves and defined over the field of rational numbers that have good and ordinary reduction at an odd prime , and have equivalent, irreducible mod Galois representations, we study the variation of the parity of Selmer ranks and analytic ranks of and over certain number fields.
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