CM points on Shimura curves via QM-equivariant isogeny volcanoes

Abelian varieties of dimension (> 1) (11G10) Complex multiplication and moduli of abelian varieties (11G15) Arithmetic aspects of modular and Shimura varieties (11G18)

Cites Work

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Products of CM elliptic curves
Torsion of rational elliptic curves over cubic fields and sporadic points on \(X_1(n)\)
On the Hasse principle for Shimura curves
Non-elliptic Shimura curves of genus one
Arithmétique des algèbres de quaternions
On the real points of an arithmetic quotient of a bounded symmetric domain
Curves with infinitely many points of fixed degree
Integral models of certain Shimura curves
The Magma algebra system. I: The user language
Torsion points and Galois representations on CM elliptic curves
On the level of modular curves that give rise to isolated \(j\)-invariants
Moduli and fibre systems of abelian varieties
Construction of class fields and zeta functions of algebraic curves
Ramification in division fields and sporadic points on modular curves
Isogeny volcanoes
Shimura curves of genus at most two
A linear lower bound on the gonality of modular curves
Uniformizing functions for certain Shimura curves, in the case D=6
Produkte Abelscher Varietäten und Moduln über Ordnungen.
On the structure of singular abelian varieties
ON A SHIMURA CURVE THAT IS A COUNTEREXAMPLE TO THE HASSE PRINCIPLE
Hasse principle violations for Atkin-Lehner twists of Shimura curves
Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
Quaternion Orders, Quadratic Forms, and Shimura Curves
TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE)
Quaternion Algebras
Equations of hyperelliptic Shimura curves
On the Field of Rationality for an Abelian Variety
Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves
The least degree of a CM point on a modular curve
Odd degree isolated points on \(X_1(N)\) with rational \(j\)-invariant

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