论文标题
LMFDB中的等级2属2属的合理点
Rational points on rank 2 genus 2 bielliptic curves in the LMFDB
论文作者
论文摘要
在Balakrishnan，Dogra和第一作者的作品的基础上，我们为明确的二次Chabauty方法提供了一些改进，以计算$ 2 $ 2 $ bielliptic曲线的合理点，超过$ \ Mathbb {q} $，其Jacobians的Jacobians的Mordell-Weil等级等于$ 2 $。我们通过精确分析对此进行补充，以确保正确的输出。与Mordell-Weil筛子一起，这种Bielliptic二次chabauty方法是我们使用的主要工具，用于计算从LMFDB $ 411 $的$ 411 $上的合理点，从而满足上述条件。
Building on work of Balakrishnan, Dogra, and of the first author, we provide some improvements to the explicit quadratic Chabauty method to compute rational points on genus $2$ bielliptic curves over $\mathbb{Q}$, whose Jacobians have Mordell-Weil rank equal to $2$. We complement this with a precision analysis to guarantee correct outputs. Together with the Mordell-Weil sieve, this bielliptic quadratic Chabauty method is then the main tool that we use to compute the rational points on the $411$ locally solvable curves from the LMFDB which satisfy the aforementioned conditions.
