Local invariants (reviewed)

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 $1$.