论文标题
沃特金斯（Watkins）对主要电力导体的椭圆曲线二次曲折的猜想
Watkins's conjecture for quadratic twists of Elliptic Curves with Prime Power Conductor
论文作者
论文摘要
沃特金斯的猜想断言，椭圆曲线的等级是由其模块化度的$ 2 $ addic估值的上限。我们表明，当$ e $是椭圆形曲线的任何二次转折时，有理性的$ 2 $ torsion和Prime Power导体的任何二次转折时，就会满足这种猜想。此外，我们给出了$ y^2 = x^3-dx $的椭圆形曲线的一致性曲线的下限，并带有$ d $ a biquadratefree整数。
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 of an elliptic curve with rational $2$-torsion and prime power conductor. Furthermore, we give a lower bound of the congruence number for elliptic curves of the form $y^2=x^3-dx$, with $d$ a biquadratefree integer.
