Bielliptic modular curves X0* (N)

Autor: Bars Cortina, Francesc, González Rovira, Josep

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

Let N = 1 be a integer such that the modular curve X* 0 (N) has genus = 2. We prove that X* 0 (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X* 0 (N) is bielliptic over the base field for all these values of N, except X*

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::2ea83f8aef6be0bb2baf7c83a97af7b2
https://ddd.uab.cat/record/240651

Bielliptic modular curves $X_0^*(N)$ with square-free levels

Autor: Josep González Rovira, Francesc Bars

Publikováno v: Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

Let $N\geq 1$ be a square-free integer such that the modular curve $X_0^*(N)$ has genus $\geq 2$. We prove that $X_0^*(N)$ is bielliptic exactly for $19$ values of $N$, and we determine the automorphism group of these bielliptic curves. In particular

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::42e9b7a56bb1dc1e6d337e01e124d384

Local Points on Shimura Coverings of Shimura Curves at Bad Reduction Primes

Autor: Vera Piquero, Carlos de

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Scopus-Elsevier

Let XD be the Shimura curve associated with an indefinite rational quaternion algebra of reduced discriminant D>1. For each prime l|D, there is a natural cyclic Galois covering of Shimura curves XD,l → XD constructed by adding certain level structu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::71cd16cf397a50411b0db58f1b91912b

Integral points of a modular curve of level 11

Autor: René Schoof, Nikos Tzanakis

Using lower bounds for linear forms in elliptic logarithms we determine the integral points of the modular curve associated to the normalizer of a non-split Cartan group of level 11. As an application we obtain a new solution of the class number one

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f54a968bb6d3a1dcebbee3881424014f
http://hdl.handle.net/2108/102829

Telegraphic reviews.

Autor: Ostebee, Arnold, Zorn, Paul

Publikováno v: American Mathematical Monthly. Feb1994, Vol. 101 Issue 2, p191. 3p.