• Equations of bielliptic modular curves 

    González Rovira, Josep (2012-11)
    Article
    Accés obert
    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 

    Dieulefait, Luis Victor; Gonzalez Jimenez, Enrique; Jiménez Urroz, Jorge (2011-06)
    Article
    Accés obert
    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 

    Molina Blanco, Santiago (2012)
    Article
    Accés obert
    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 

    David, Chantal; Jiménez Urroz, Jorge (2010-09)
    Article
    Accés obert
    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 

    Molina Blanco, Santiago; González Rovira, Josep (2015)
    Article
    Accés obert
    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 ...