Now showing items 1-7 of 7

• #### Automorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes ﻿

(2014)
Article
Open Access
The aim of this short note is to show how the interplay of the action of the automorphism group of a Shimura curve on the special fiber of its Cerednik-Drinfeld’s integral model at a prime of bad reduction and its sets ...
• #### Computation of ATR Darmon points on nongeometrically modular elliptic curves ﻿

(2013-03)
Article
Restricted access - publisher's policy
ATR points were introduced by Darmon as a conjectural con- struction of algebraic points on certain elliptic curves for which the Heegner-point method is not in general available. So far, the only numerical evidence, ...
• #### 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.
• #### On fields of definition of torsion points of elliptic curves with complex multiplication ﻿

(2011-06)
Article
Open Access
For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of ...
• #### Ribet Bimodules and the Specialization of Heegner points ﻿

(2012)
Article
Open Access
For a given order R in an imaginary quadratic field K, we study the specialization of the set CM(R) of Heegner points on the Shimura curve X = X0(D,N) at primes p | DN. As we show, if p does not divide the conductor of R, ...
• #### Square-free discriminants of Frobenius rings ﻿

(2010-09)
Article
Open Access
Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of $E_p$, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field $Q(\pi_p)$ generated ...
• #### The kernel of Ribet’s isogeny for genus three Shimura curves ﻿

(2015)
Article
Open Access
There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine ...