Open AccessParity of ranks of elliptic curves with equivalent mod đť‘ť Galois representations
Author(s) -
Sudhanshu Shekhar
Publication year - 2016
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/12993
Subject(s) - algorithm , annotation , computer science , artificial intelligence , mathematics
Given two elliptic curves E 1 E_1 and E 2 E_2 defined over the field of rational numbers Q \mathbb {Q} that have good and ordinary reduction at an odd prime p p , and have equivalent, irreducible mod p p Galois representations, we study the variation of the parity of Selmer ranks and analytic ranks of E 1 E_1 and E 2 E_2 over certain number fields.