Non-elliptic Shimura curves of genus one

DOI10.2969/jmsj/1179759530zbMath1123.11019arXivmath/0612732OpenAlexW2019598894MaRDI QIDQ861742

Josep González, Victor Rotger

Publication date: 30 January 2007

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612732

zbMATH Keywords

elliptic curveShimura curvecomplex multiplication pointscurve of genus one

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items (11)

Arithmetic $(1;e)$-curves and Belyĭ maps ⋮ The kernel of Ribet's isogeny for genus three Shimura curves ⋮ Equations of hyperelliptic Shimura curves ⋮ Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves ⋮ Canonical models of arithmetic \((1; e)\)-curves ⋮ Points on Shimura curves rational over imaginary quadratic fields in the non-split case ⋮ Automorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes ⋮ Ribet bimodules and the specialization of Heegner points ⋮ Ramanujan-type \(1/\pi\)-series from bimodular forms ⋮ RATIONAL POINTS ON SHIMURA CURVES AND THE MANIN OBSTRUCTION ⋮ An effective bound of p for algebraic points on Shimura curves of \varGamma₀(p)-type

Uses Software

• Magma

Cites Work

• Local diophantine properties of Shimura curves
• Arithmétique des algèbres de quaternions
• On the real points of an arithmetic quotient of a bounded symmetric domain
• Construction of class fields and zeta functions of algebraic curves
• On canonical models of arithmetic quotients of bounded symmetric domains
• On finiteness conjectures for endomorphism algebras of abelian surfaces
• Genus 2 Curves with Quaternionic Multiplication
• ON p-ADIC POINCARÉ SERIES AND SHIMURA CURVES
• Uniformization of certain Shimura curves
• Modular Shimura varieties and forgetful maps
• Minimal Models for 2-coverings of Elliptic Curves
• Algorithmic Number Theory
• Classical invariants and 2-descent on elliptic curves
• Heegner points on Mumford-Tate curves
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