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.
Equations and rational points of the modular curves X_0^+(p) / Mercuri, Pietro. - In: THE RAMANUJAN JOURNAL. - ISSN 1572-9303. - 47:2(2018), pp. 291-308. [10.1007/s11139-017-9925-2]
Equations and rational points of the modular curves X_0^+(p)
MERCURI, PIETRO
2018
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_Equations-and-rational_2018.pdf
solo gestori archivio
Note: articolo
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
452.19 kB
Formato
Adobe PDF
|
452.19 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
