Carlos Castaño-Bernard

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Fix a positive integer N and let X0(N) be the moduli space of (ordered) pairs (E,E ) of generalised elliptic curves E and E ′ linked by a cyclic isogeny φ : E −→ E ′ of degree N . Consider the Atkin-Lehner quotient curve X 0 (N) defined by the involution wN of X0(N) induced by mapping an isogeny φ : E −→ E ′ to its dual φ̂ : E ′ −→ E. The quotient curve X 0(More)
Certain identities of Ramanujan may be succinctly expressed in terms of the rational function ğχ = f̆χ − 1 f̆χ on the modular curve X0(N), where f̆χ = wNfχ and fχ is a certain modular unit on the Nebentypus cover Xχ(N) introduced by Ogg and Ligozat for prime N ≡ 1 (mod 4) and wN is the Fricke involution. These correspond to levels N = 5, 13, where the genus(More)
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)
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