1Function: elltamagawa
2Section: elliptic_curves
3C-Name: elltamagawa
4Prototype: G
5Help: elltamagawa(E): E being an elliptic curve over a number field,
6 returns the global Tamagawa number of the curve.
7Doc:
8 The object $E$ being an elliptic curve over a number field, returns the global
9 Tamagawa number of the curve (including the factor at infinite places).
10 \bprog
11 ? e = ellinit([1, -1, 1, -3002, 63929]); \\ curve "90c6" from elldata
12 ? elltamagawa(e)
13 %2 = 288
14 ? [elllocalred(e,p)[4] | p<-[2,3,5]]
15 %3 = [6, 4, 6]
16 ? vecprod(%)  \\ since e.disc > 0 the factor at infinity is 2
17 %4 = 144
18 @eprog
19