تقرير
Towards a classification of isolated $j$-invariants
| العنوان: | Towards a classification of isolated $j$-invariants |
|---|---|
| المؤلفون: | Bourdon, Abbey, Hashimoto, Sachi, Keller, Timo, Klagsbrun, Zev, Lowry-Duda, David, Morrison, Travis, Najman, Filip, Shukla, Himanshu |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | We develop an algorithm to test whether a non-CM elliptic curve $E/\mathbb{Q}$ gives rise to an isolated point of any degree on any modular curve of the form $X_1(N)$. This builds on prior work of Zywina which gives a method for computing the image of the adelic Galois representation associated to $E$. Running this algorithm on all elliptic curves presently in the $L$-functions and Modular Forms Database and the Stein-Watkins Database gives strong evidence for the conjecture that $E$ gives rise to an isolated point on $X_1(N)$ if and only if $j(E)=-140625/8, -9317,$ $351/4$, or $-162677523113838677$. Comment: With an appendix by Maarten Derickx and Mark van Hoeij, to appear in Math. Comp |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.07740 |
| رقم الأكسشن: | edsarx.2311.07740 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |