Proposition 16.2.
There is a group homomorphism
E
′
(
K
)
→
K
∗
∕
(
K
∗
)
2
(
x
,
y
)
↦
{
x
mod
(
K
∗
)
2
if
x
≠
0
b
′
mod
(
K
∗
)
2
if
x
=
0
with
kernel
ϕ
E
(
K
)
.