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math.NT2022
On the fibres of an elliptic surface where the rank does not jump
Jerson Caro, Hector Pasten
For a non-constant elliptic surface over defined over , it is a result of Silverman that the Mordell--Weil rank of the fibres is at least the rank of the…
math.NT2022
Watkins's conjecture for quadratic twists of Elliptic Curves with Prime Power Conductor
Jerson Caro
Watkins' conjecture asserts that the rank of an elliptic curve is upper bounded by the -adic valuation of its modular degree. We show that this conjecture is satisfied when …
math.NT2022
Watkins' conjecture for elliptic curves over function fields
Jerson Caro
In 2002 Watkins conjectured that given an elliptic curve defined over , its Mordell-Weil rank is at most the -adic valuation of its modular degree. We consider the a…