Now showing items 1-20 of 38

• #### Automorphism group of split Cartan modular curves ﻿

(2016-08-01)
Article
Open Access
• #### Bielliptic modular curves X-0*(N) ﻿

(2020-10-01)
Article
Open Access
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 ...
• #### Bielliptic modular curves X-0*(N) with square-free levels ﻿

(2019-11-01)
Article
Open Access
Let N=1 be a square-free integer such that the modular curve X*0(N) has genus =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 ...
• #### Bielliptic quotient modular curves with N square-free ﻿

(2020-11)
Article
Open Access
Let N = 1 be an square free integer and let WN be a non-trivial subgroup of the group of the Atkin-Lehner involutions of X0(N) such that the modular curve X0(N)/WN has genus at least two. We determine all pairs (N, WN ) ...
• #### CAAV. Activitat 2 (Curs 2016/2017 - Q2) ﻿

(Universitat Politècnica de Catalunya, 2017-04-06)
Exam
• #### CAAV. Activitat 2 (Curs 2017/2018 - Q1)  ﻿

(Universitat Politècnica de Catalunya, 2017-11-08)
Exam
• #### CAAV. Activitat 2 (Curs 2017/2018 - Q2)  ﻿

(Universitat Politècnica de Catalunya, 2018-04-16)
Exam
• #### CAAV. Activitat 2 (Curs 2018/2019 - Q2)  ﻿

(Universitat Politècnica de Catalunya, 2019-03-29)
Exam
• #### CAAV. Activitat 3 i 4 (Curs 2016/2017 - Q2)  ﻿

(Universitat Politècnica de Catalunya, 2017-06-19)
Exam
• #### CAAV. Activitat 3 i 4 (Curs 2017/2018 - Q1)  ﻿

(Universitat Politècnica de Catalunya, 2018-01-08)
Exam
• #### CAAV. Activitat 3 i 4 (Curs 2017/2018 - Q2)  ﻿

(Universitat Politècnica de Catalunya, 2018-06-01)
Exam
• #### CAAV. Reavaluació (Curs 2017/2018 - Q2)  ﻿

(Universitat Politècnica de Catalunya, 2018-06-19)
Exam
• #### CÀLCUL AVANÇAT (Examen 2n quadrimestre): Activitat 3/Activitat 4 de CAAV  ﻿

(Universitat Politècnica de Catalunya, 2019-06-11)
Exam
• #### Constraints on the automorphism group of a curve ﻿

(2017-01-01)
Article
Open Access
For a curve of genus > 1 defined over a finite field, we present a sufficient criterion for the non-existence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the ...
• #### Cropping Euler factors of modular L-functions ﻿

(2013-09)
Article
Open Access
According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian variety, then its L-function must capture a substantial part of the properties of A. The smallest number field L where A has all its endomorphisms ...
• #### Equations of bielliptic modular curves ﻿

(2012-11)
Article
Open Access
We give a procedure to determine equations for the modular curves X0(N) which are bielliptic and equations for the 30 values of N such that X0(N) is bielliptic and nonhyperelliptic are presented.
• #### Frobenius distribution for quotients of Fermat curves of prime exponent ﻿

(2015-06-18)
Article
Open Access
Let C denote the Fermat curve over Q of prime exponent l. The Jacobian Jac(C) of C splits over Q as the product of Jacobians Jac(C_k), 0< k < l-1, where C_k are curves obtained as quotients of C by certain subgroups of ...
• #### Functions and differentials on the non-split Cartan modular curve of level 11 ﻿

(2017-01-01)
Article
Open Access
The genus 4 modular curve Xns(11) attached to a non-split Cartan group of level 11 admits a model defined over Q. We compute generators for its function field in terms of Siegel modular functions. We also show that its ...
• #### Hyperelliptic parametritzations of Q-curves ﻿

(2020-07-24)
Article
Open Access
For a square-free integer N, we present a procedure to compute Q-curves parametrized by rational points of the modular curve X* 0 (N) when this is hyperelliptic.
• #### Hyperelliptic parametrizations of Q -curves ﻿

(2020-07-24)
Article
Open Access
For a square-free integer N, we present a procedure to compute Q-curves parametrized by rational points of the modular curve X∗0(N) when this is hyperelliptic