IONICA, Sorina; KILIÇER, Pınar; LAUTER, Kristin; LORENZO GARCÍA, Elisa; MÂNZĂŢEANU, Adelina; VINCENT, Christelle

doi:10.1093/qmath/haae005

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Licence d’utilisation du document

IONICA, Sorina
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]

KILIÇER, Pınar
Lithe and fast algorithmic number theory [LFANT]
Universiteit Leiden = Leiden University
Analyse cryptographique et arithmétique [CANARI]

LAUTER, Kristin
Université de Neuchâtel = University of Neuchatel [UNINE]
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]

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Article de revue

Ce document a été publié dans

Quarterly Journal of Mathematics. 2024-03-05

Oxford University Press (OUP)

Résumé en anglais

In this paper, we introduce a new problem called the Isogenous Embedding Problem (IEP) and relate the existence of solutions to this problem to the primes of bad reduction of complex multiplication curves of genus 3. More precisely, the absence of solutions to IEP implies potentially good reduction. We propose an algorithm for computing the solutions to the IEP and run the algorithm through different families of curves. Using this algorithm, we were able to prove the reduction type of some particular curves at certain primes that were open cases in R. Lercier, Q. Liu, E. Lorenzo García and C. Ritzenthaler, Reduction type of smooth plane quartics, Algebra Number Theory 15 no. 6 2021, 1429–1468.< Réduire