Abstract
AbstractLet $$d\ge 1$$
d
≥
1
be an integer and let p be a rational prime. Recall that p is a torsion prime of degree d if there exists an elliptic curve E over a degree d number field K such that E has a K-rational point of order p. Derickx et al. (Algebra Number Theory 17(2):267–308, 2023) have computed the torsion primes of degrees 4, 5, 6 and 7. We verify that the techniques used in Derickx et al. (Algebra Number Theory 17(2):267–308, 2023) can be extended to determine the torsion primes of degree 8.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Reference16 articles.
1. Anni, S., Siksek, S.: Modular elliptic curves over real abelian fields and the generalized Fermat equation $$x^{2\ell }+y^{2m}=z^p$$. Algebra Number Theory 10(6), 1147–1172 (2016)
2. Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24, 235–265 (1997). Computational algebra and number theory (London, 1993)
3. Conrad, B., Edixhoven, B., Stein, W.: $$J_1(p)$$ has connected fibers. Doc. Math. 8, 331–408 (2003)
4. Derickx, M.: Torsion points on elliptic curves over number fields of small degree. PhD thesis, Universiteit Leiden (2016)
5. Derickx, M., Kamienny, S., Stein, W., Stoll, M.: Torsion points on elliptic curves over number fields of small degree. Algebra Number Theory 17(2), 267–308 (2023)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Primitive algebraic points on curves;Research in Number Theory;2024-06-05