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changed question to reflect that the conductor of the Jacobian is the conductor of interest
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Johnson-Leung
Johnson-Leung
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It is my understanding that if I twist a hyperelliptic curve of genus 2 andwhose Jacobian has conductor $N$ by a prime $p$ with $p\nmid N$, that the conductor of the Jacobian of the twist is expected to be $Np^4$, but I am unable to find a reference for this. Is anyone aware of a proof of this "fact"?

It is my understanding that if I twist a hyperelliptic curve of genus 2 and conductor $N$ by a prime $p$ with $p\nmid N$, that the conductor of the twist is expected to be $Np^4$, but I am unable to find a reference for this. Is anyone aware of a proof of this "fact"?

It is my understanding that if I twist a hyperelliptic curve of genus 2 whose Jacobian has conductor $N$ by a prime $p$ with $p\nmid N$, that the conductor of the Jacobian of the twist is expected to be $Np^4$, but I am unable to find a reference for this. Is anyone aware of a proof of this "fact"?

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Daniel Loughran
Daniel Loughran
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Johnson-Leung
Johnson-Leung
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Reference Request: Conductors of Twists of Hyperelliptic Curves

It is my understanding that if I twist a hyperelliptic curve of genus 2 and conductor $N$ by a prime $p$ with $p\nmid N$, that the conductor of the twist is expected to be $Np^4$, but I am unable to find a reference for this. Is anyone aware of a proof of this "fact"?