In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup Γ 0 (N), with respect to the usual fundamental domain F N , where N is assumed prime. The cycles Q 1 ,. .. , Q n that this algorithm produces are such that the the corresponding paths γ 1 ,. .. , γ n in the Riemann surface X 0 (N)(C) have… (More)
Let C be the image of a canonical embedding φ of the Atkin-Lehner quotient X + 0 (N) associated to the Fricke involution w N. Suppose φ is defined over the rationals. In this note we give some collinearity relations among rational points of C, for each X + 0 (N) of genus 3 and the first X + 0 (N) of genus 4, for N prime.
Let E be an elliptic curve of conductor N and rank one over Q. So there is a non-constant morphism X
Certain identities of Ramanujan may be succinctly expressed in terms of the rational function ˘ g χ = ˘ f χ −
Let E be an elliptic curve defined over the rationals and let N be its conductor. Assume N is prime. In this paper we give numerical evidence that suggests some conjectures on the 2-divisibility of certain sums of Heenger points of discriminant D dividing 4N on the elliptic curve E. One of these conjectures suggests a possible link between the parity of the… (More)