For any positive integer N, we completely determine the structure of the rational cuspidal
divisor class group of X 0 (N), which is conjecturally equal to the rational torsion subgroup of …

Let $ E $ be an elliptic curve over the rational numbers. Watkins [Experiment. Math. 11
(2002), pp. 487–502 (2003)] conjectured that the rank of $ E $ is bounded by the $2 $-adic …

Watkins conjectured that for an elliptic curve $ E $ over $\mathbb {Q} $ of Mordell-Weil rank
$ r $, the modular degree of $ E $ is divisible by $2^ r $. If $ E $ has non-trivial rational $2 …

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 …

In 2002 Watkins conjectured that given an elliptic curve defined over Q, its Mordell–Weil
rank is at most the 2-adic valuation of its modular degree. We consider the analogous …

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 …

Watkins's conjecture suggests that for an elliptic curve $ E/\mathbb {Q} $, the rank of the
group $ E (\mathbb {Q}) $ of rational points is bounded above by $\nu_2 (m_E) $, where …

SOME ADVANCES IN A CONJECTURE OF WATKINS AND AN ANALOGUE OVER FUNCTION
FIELDS Page 1 FACULTAD DE MATEM ATICAS SOME ADVANCES IN A CONJECTURE OF …

For any positive integer $ N $, we completely determine the structure of the rational cuspidal
divisor class group of $ X_0 (N) $, which is conjecturally equal to the rational torsion …

The mistake arose from a misunderstanding of the paper of Yazadani [2, Theorem 3.8]
where he proves an assertion about the congruence number and not the modular degree …