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arXiv · 2212.14083

Determining the primes of bad reduction of CM curves of genus 3

Sorina Ionica·Pinar Kiliçer·Kristin Lauter·Elisa Lorenzo García·Adelina Mânzăţeanu·Christelle Vincent
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Abstract

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 curves of genus $3$ and we can detect potentially good reduction in absence of solutions. We propose an algorithm for computing the solutions to the IEP and run the algorithm through different families of curves. We were able to prove the reduction type of some particular curves at certain primes that were open cases in [LLLR21].

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Sorina Ionica, Pinar Kiliçer, Kristin Lauter, Elisa Lorenzo García, Adelina Mânzăţeanu, Christelle Vincent. 2022-12-28. Determining the primes of bad reduction of CM curves of genus 3. https://arxiv.org/abs/2212.14083

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