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<p>In this paper we determine the conductor exponent of non-special Ciani quartics at primes of potentially good reduction in terms of the Ciani invariants. As an intermediate step in order to do so, we provide a reconstruction algorithm to construct Ciani quartics with given invariants. We also discuss how to descend the provided model to be defined over the same field as the invariants.</p>

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On the Conductor of Ciani Plane Quartics

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Irene Bouw,
  • Nirvana Coppola,
  • Elisa Lorenzo García,
  • Anna Somoza

摘要

In this paper we determine the conductor exponent of non-special Ciani quartics at primes of potentially good reduction in terms of the Ciani invariants. As an intermediate step in order to do so, we provide a reconstruction algorithm to construct Ciani quartics with given invariants. We also discuss how to descend the provided model to be defined over the same field as the invariants.