#### Filter Results:

- Full text PDF available (5)

#### Publication Year

2005

2009

- This year (0)
- Last 5 years (0)
- Last 10 years (2)

#### Publication Type

#### Journals and Conferences

Learn More

- Carlos Castaño-Bernard
- Experimental Mathematics
- 2009

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 of conductor N and rank one over Q. So there is a non-constant morphism X 0 (N) −→ E defined over Q, where X 0 (N) = X0(N)/wN and wN is the Fricke involution. Under this morphism the traces of the Heegner points of X 0 (N) map to rational points on E. In this paper we study the index I of the subgroup generated by all these traces… (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)

In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup Γ(N), with respect to the usual fundamental domain FN , where N is assumed prime. The cycles Q1, . . . , Qn that this algorithm produces are such that the the corresponding paths γ1, . . . , γn in the Riemann surface X0(N)(C) have a nice… (More)

- ‹
- 1
- ›