Year: 2025
Type: article
Abstract: Watkins’s conjecture asserts that the rank of an elliptic curve is upper bounded by the 2 -adic valuation of its modular degree. We show that this conjecture is satisfied when E is any quadratic twist of an elliptic curve with a rational point of order 2 and prime power conductor, in particular, for the congruent number elliptic curves. Furthermore, we give a lower bound for the congruence number for elliptic curves of the form y 2 = x 3 - d x , with d a fourth power free integer.
DOI: 10.5802/jtnb.1335
Author: Jerson Caro
Institution: Boston University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414358001