@article{LENG2024, 
author = {Mingrui LENG and Yongfeng FAN and Li CAI},
title = {Quadratic twists of the elliptic curve 14a2},
year = {2024},
journal = {Journal of Capital Normal University (Natural Science Edition)},
volume = {45},
number = {6},
pages = {2-8},
keywords = {elliptic curve, Selmer group, Heegner point},
url = {https://www.sciopen.com/article/10.19789/j.1004-9398.2024.06.001},
doi = {10.19789/j.1004-9398.2024.06.001},
abstract = {In this paper, we consider a quadratic twist family of the elliptic curve 14a2. Using the classical 2-descent method, we prove that all curves in this family have 2-Selmer group (Z/2Z)2. Assume the finiteness of the Shafarevich-Tate group, then these curves have rank 1, Selmer Z2-corank 1, and trivial 2-primary part of the Shafarevich-Tate group. According to the Gross-Zagier formula and the Tunnell-Saito theorem, we raise the question of how to prove the non-triviality of certain explicit Heegner points defined on Shimura curves associated to the quaternion algebra precisely ramified at 2 and 7.}
}