Corollary 7.3.
Assuming that:
E
∕
𝔽
q
an
elliptic curve
ϕ
∈
End
(
E
)
the
q
-power Frobenius
Then
#
E
(
𝔽
q
)
=
q
+
1
−
tr
(
ϕ
)
and
|
tr
(
ϕ
)
|
≤
2
q
.