Proposition 2.7.
Assuming that:
K
=
K
¯
,
char
K
≠
2
C
⊂
ℙ
2
a smooth plane cubic
P
∈
C
a point of inflection
Then
we may change coordinates such that
C
:
Y
2
Z
=
X
(
X
−
Z
)
(
X
−
λ
Z
)
for some
λ
≠
0
,
1
and
P
=
(
0
:
1
:
0
)
.