Browsing by Subject "Curves, Elliptic"
Now showing items 47 of 7

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 ...