论文标题
椭圆曲线，在前六个素数之外有良好的减少
Elliptic curves with good reduction outside of the first six primes
论文作者
论文摘要
我们提出了一个有理椭圆曲线的数据库，直至Q-异态性，在{2,3,5,7,11,13}之外，大幅减少。我们提供了一种涉及ABC和BSD猜想的启发式方法，即数据库可能是此类曲线的完整集。此外，证明完整性可能只需要更多的计算时间就可以得出结论。我们介绍有关集合中与曲线相关的各种数量分布的数据。我们还讨论了与S-UNIT方程的联系以及具有最大导体的有理椭圆曲线的存在。
We present a database of rational elliptic curves, up to Q-isomorphism, with good reduction outside {2,3,5,7,11,13}. We provide a heuristic involving the abc and BSD conjectures that the database is likely to be the complete set of such curves. Moreover, proving completeness likely needs only more computation time to conclude. We present data on the distribution of various quantities associated to curves in the set. We also discuss the connection to S-unit equations and the existence of rational elliptic curves with maximal conductor.
