تقرير
Towards a classification of isolated $j$-invariants
العنوان: | Towards a classification of isolated $j$-invariants |
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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. |