24 citations · 42 across the 9 of their papers we have counts for
7 papers · 1 filter
Determining the primes of bad reduction of CM curves of genus 3
Sorina Ionica, Pinar Kiliçer, Kristin Lauter +3
In this paper we introduce a new problem called the Isogenous Embedding Problem (IEP). The existence of solutions to this problem is related to the primes of bad reduction of CM cu…
Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication
Bogdan Dina, Sorina Ionica, Jeroen Sijsling
We analyze complex multiplication for Jacobians of curves of genus 3, as well as the resulting Shimura class groups and their subgroups corresponding to Galois conjugation over the…
Genus 3 hyperelliptic curves with CM via Shimura Reciprocity
B. Dina, S. Ionica
Up to isomorphism over C, every simple principally polarized abelian variety of dimension 3 is the Jacobian of a smooth projective curve of genus 3. Furthermore, this curve is eith…
Modular invariants for genus 3 hyperelliptic curves
Sorina Ionica, Pinar Kilicer, Kristin Lauter +4
In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary oc-tics to Siegel modular forms of genus 3. W…
Constructing genus 3 hyperelliptic Jacobians with CM
Jennifer S. Balakrishnan, Sorina Ionica, Kristin Lauter +1
Given a sextic CM field , we give an explicit method for finding all genus 3 hyperelliptic curves defined over whose Jacobians are simple and have complex multiplic…
Isogeny graphs with maximal real multiplication
Sorina Ionica, Emmanuel Thomé
An isogeny graph is a graph whose vertices are principally polarized abelian varieties and whose edges are isogenies between these varieties. In his thesis, Kohel described the str…
Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
Sorina Ionica
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the -Tate pairing in terms of the action of the Frobenius on the -torsion of…