由三角数产生的椭圆曲线。

Q4 Mathematics

Integers Pub Date : 2019-01-01

Abhishek Juyal, Shiv Datt Kumar, Dustin Moody

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引用次数: 0

摘要

我们研究了椭圆曲线的勒让德族Et:y2=x（x-1）（x-Δt），其参数为三角数Δt=t（t+1）/2。我们证明了Et在函数域Q-（t）上的秩为1，而在Q（t）之上的秩为0。我们还产生了一些无限的亚家族，它们的Mordell-Weil秩是正的，并从这些家族中找到了高秩曲线。

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ELLIPTIC CURVES ARISING FROM THE TRIANGULAR NUMBERS.

We study the Legendre family of elliptic curves E_t : y ² = x(x - 1)(x - Δ _t ), parametrized by triangular numbers Δ _t = t(t + 1)/2. We prove that the rank of E_t over the function field $\overset{‒}{Q} (t)$ is 1, while the rank is 0 over $Q (t)$ . We also produce some infinite subfamilies whose Mordell-Weil rank is positive, and find high rank curves from within these families.

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来源期刊

Integers Mathematics-Discrete Mathematics and Combinatorics

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

50 weeks