WATKINS'S CONJECTURE FOR ELLIPTIC CURVES WITH NON-SPLIT MULTIPLICATIVE REDUCTION

被引：2

作者：

Caro, Jerson ^{[1
]}

Pasten, Hector ^{[2
]}

机构：

[1] Pontificia Univ Catolica Chile, Fac Matemat, Dept Matemat, 4860 Ave Vicuna Mackenna, Macul, RM, Chile

[2] Pontificia Univ Catolica Chile, Dept Matemat, Fac Matem, Macul, RM, Chile

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 08期

关键词：

Watkins's conjecture; modular degree; rank; parity conjecture; MODULAR DEGREE;

D O I：

10.1090/proc/15942

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 valuation of the modular degree of E. We prove this conjecture for semistable elliptic curves having exactly one rational point of order 2, provided that they have an odd number of primes of non-split multiplicative reduction or no primes of split multiplicative reduction.

引用

页码：3245 / 3251

页数：7

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