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Computational Number Theory is for explicit calculations or algorithms involving anything of interest to number theorists.

2 votes
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Conductor of hyperelliptic curve after base change

Let $r\geq 5$ be a prime, and let $\zeta$ denote a primitive $r$-th root of unity. Let $C$ be a hyperelliptic curve defined over $\mathbb{Q}$. Suppose I have computed the conductor exponent $n$ of $C/ …
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2 votes
0 answers
54 views

Conductor of hyperelliptic curve after adding a rational root

Let $r\geq 5$ be a prime. Suppose I have a specified hyperelliptic curve $C: y^2=f(x)$ defined over $\mathbb{Q}$, where $f\in\mathbb{Q}[x]$ has degree $r$. Note: the roots of $f$ are not rational but …
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