33 citations · 51 across the 9 of their papers we have counts for
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Isogenies on Kummer Surfaces
Maria Corte-Real Santos, E. Victor Flynn
We first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient (N,N)-isogenies, for any odd N, both…
An analog of the Edwards model for Jacobians of genus 2 curves
E. Victor Flynn, Kamal Khuri-Makdisi
We give the explicit equations for a P^3 x P^3 embedding of the Jacobian of a curve of genus 2, which gives a natural analog for abelian surfaces of the Edwards curve model of elli…
Arbitrarily large -torsion in Tate-Shafarevich groups
E. Victor Flynn, Ari Shnidman
We show that, for any prime , there exist absolutely simple abelian varieties over with arbitrarily large -torsion in their Tate-Shafarevich group. To prove this…
Genus two curves with full -level structure and Tate-Shafarevich groups
Nils Bruin, E. Victor Flynn, Ari Shnidman
We give an explicit rational parameterization of the surface over whose points parameterize genus 2 curves~ with full -level structure on…
Descent via (3,3)-isogeny on Jacobians of genus 2 curves
Nils Bruin, E. Victor Flynn, Damiano Testa
We give parametrisation of curves C of genus 2 with a maximal isotropic (ZZ/3)^2 in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent v…
Finite Weil restriction of curves
E. V. Flynn, D. Testa
Given number fields , smooth projective curves defined over and defined over , and a non-constant -morphism ,we consider the curv…
Two-coverings of Jacobians of curves of genus two
E. Victor Flynn, Damiano Testa, Ronald van Luijk
We find explicit equations for two-coverings of Jacobians of genus two curves over an arbitrary ground field of characteristic different from two.
On finiteness conjectures for endomorphism algebras of abelian surfaces
Nils Bruin, E. Victor Flynn, Josep Gonzalez +1
It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this…
Cycles of Quadratic Polynomials and Rational Points on a Genus-Two Curve
E. V. Flynn, Bjorn Poonen, Edward F. Schaefer
It has been conjectured that for sufficiently large, there are no quadratic polynomials in with rational periodic points of period . Morton proved there were no…