On a special case of Watkins' conjecture

  title={On a special case of Watkins' conjecture},
  author={Matija Kazalicki and Daniela Kohen},
  journal={arXiv: Number Theory},
Watkins' conjecture asserts that for a rational elliptic curve $E$ the degree of the modular parametrization is divisible by $2^r$, where $r$ is the rank of $E$. In this paper we prove that if the modular degree is odd then $E$ has rank $0$. Moreover, we prove that the conjecture holds for all rank two rational elliptic curves of prime conductor and positive discriminant. 
3 Citations

Watkins's conjecture for quadratic twists of Elliptic Curves with Prime Power Conductor

. Watkins’ 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

A conjecture of Watkins for quadratic twists

Watkins conjectured that for an elliptic curve E over Q of Mordell-Weil rank r, the modular degree of E is divisible by 2. If E has non-trivial rational 2-torsion, we prove the conjecture for all the

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La méthode des graphes

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