Browsing by Subject "Curves, Elliptic"
Now showing items 17 of 7

Automorphisms and reduction of Heegner points on Shimura curves at CerednikDrinfeld primes
(2014)
Article
Open AccessThe 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 CerednikDrinfeld’s integral model at a prime of bad reduction and its sets ... 
Computation of ATR Darmon points on nongeometrically modular elliptic curves
(201303)
Article
Restricted access  publisher's policyATR points were introduced by Darmon as a conjectural con struction of algebraic points on certain elliptic curves for which the Heegnerpoint method is not in general available. So far, the only numerical evidence, ... 
Equations of bielliptic modular curves
(201211)
Article
Open AccessWe 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
(201106)
Article
Open AccessFor 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 AccessFor 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, ... 
Squarefree discriminants of Frobenius rings
(201009)
Article
Open AccessLet 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 AccessThere 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 ...