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TITLE Quadratic twists of X-0(14)
KIAS AUTHORS Choi, Junhwa
JOURNAL JOURNAL OF NUMBER THEORY, 2021
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ABSTRACT In the present paper, we prove the 2-part of Birch and Swinnerton-Dyer conjecture for an explicit infinite family of rank 0 quadratic twists of the modular elliptic curve X-0(14), using an explicit form of the Waldspurger formula. We also give an explicit infinite family of rank 1 quadratic twists of X-0(14) whose Tate-Shafarevich group is of odd cardinality. (c) 2021 Elsevier Inc. All rights reserved.
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