Theorem 7.4.
Assuming that:
E
∕
𝔽
q
an
elliptic curve
with
#
E
(
𝔽
q
)
=
q
+
1
−
a
Then
Z
E
(
T
)
=
1
−
a
T
+
q
T
2
(
1
−
T
)
(
1
−
q
T
)
.