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A conjecture of Watkins for quadratic twists
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-03-25 , DOI: 10.1090/proc/15376 Jose A. Esparza-Lozano , Hector Pasten
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-03-25 , DOI: 10.1090/proc/15376 Jose A. Esparza-Lozano , Hector Pasten
Abstract:Watkins conjectured that for an elliptic curve 
over 
of Mordell-Weil rank 
, the modular degree of 
is divisible by 
. If 
has non-trivial rational 
-torsion, we prove the conjecture for all the quadratic twists of 
by squarefree integers with sufficiently many prime factors.
中文翻译：
关于二次扭曲的沃特金斯猜想
摘要：沃特金斯推测为椭圆曲线在莫德尔-韦伊等级的，模块化程度是整除。如果具有非平凡的有理扭转，我们证明具有足够多素数的无平方整数的所有二次扭转的猜想。
更新日期：2021-04-22
over of Mordell-Weil rank , the modular degree of is divisible by . If has non-trivial rational -torsion, we prove the conjecture for all the quadratic twists of by squarefree integers with sufficiently many prime factors. 中文翻译：
关于二次扭曲的沃特金斯猜想
摘要：沃特金斯推测为椭圆曲线
在莫德尔-韦伊等级的，模块化程度是整除。如果具有非平凡的有理扭转，我们证明具有足够多素数的无平方整数的所有二次扭转的猜想。 
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