The **local invariants** of a genus 2 curve over $\Q$ include, for each prime $p$:

- The $p$-adic valuation $\mathrm{ord}_p(\Delta)$ of its discriminant;
- The $p$-adic valuation $\mathrm{ord}_p(N)$ of the conductor of its Jacobian;
- The Tamagawa number $c_p$ ;
- The L-factor at $p$.

For primes of good reduction the valuations of both discriminant and conductor are $0$, and the Tamagawa number is $1$.

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- Review status: reviewed
- Last edited by John Cremona on 2020-01-28 12:58:26

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- 2020-01-28 12:58:26 by John Cremona (Reviewed)
- 2020-01-08 04:13:46 by John Cremona (Reviewed)
- 2020-01-04 09:10:32 by Andrew Sutherland

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