Let p be an odd prime number and let X+0 (p) be the quotient of the classical modular curve X0(p) by the action of the Atkin-Lehner operator wp. In this paper we show how to compute explicit equations for the canonical model of X+0 (p). Then we show how to compute the modular parametrization, when it exists, from X+0 (p) to an isogeny factor E of dimension 1 of its jacobian J+0 (p). Finally, we show how use this map to determine the rational points on X+0 (p) up to a large fixed height.
Mercuri, P. (2018). Equations and rational points of the modular curves X_0^+(p). THE RAMANUJAN JOURNAL, 47(2), 291-308 [10.1007/s11139-017-9925-2].
Equations and rational points of the modular curves X_0^+(p)
MERCURI, PIETRO
2018-01-01
Abstract
Let p be an odd prime number and let X+0 (p) be the quotient of the classical modular curve X0(p) by the action of the Atkin-Lehner operator wp. In this paper we show how to compute explicit equations for the canonical model of X+0 (p). Then we show how to compute the modular parametrization, when it exists, from X+0 (p) to an isogeny factor E of dimension 1 of its jacobian J+0 (p). Finally, we show how use this map to determine the rational points on X+0 (p) up to a large fixed height.
| File | Dimensione | Formato | |
|---|---|---|---|
|
Mercuri P. - Equations.pdf
Solo gestori archvio
Tipologia:
Versione Editoriale
Dimensione
466.06 kB
Formato
Adobe PDF
|
466.06 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
