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date: 2022-04-05 23:42
modification date: Tuesday 5th April 2022 23:42:25
title: "Tamagawa numbers"
aliases: [Tamagawa numbers]
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# Tamagawa numbers

Definition: for $G\in \Alg\Grp\slice k$ with $G(k)$ its $k\dash$points and $G(\AA_k)$ its [adelic](adelic) points, $\tau = \mu(G(\AA_k) / G(k))$.
Local Tamagawa number for [elliptic curve](elliptic%20curve.md) : equals 1 when the curve has [good reduction](good%20reduction.md)..
Show up in [Birch and Swinnerton-Dyer conjecture](Birch%20and%20Swinnerton-Dyer%20conjecture.md).

![Pasted image 20211106015658.png](Pasted%20image%2020211106015658.png)