Lemma 5.4.
Assuming that:
ϕ
:
E
1
→
E
2
an
isogeny
Then
there exists a morphism
ξ
making the following diagram commute:
(
x
i
=
x
-coordinate on a Weierstrass equation for
E
i
). Moreover if
ξ
(
t
)
=
r
(
t
)
s
(
t
)
,
r
,
s
∈
K
[
t
]
coprime, then
deg
ϕ
=
deg
ξ
=
max
(
deg
(
r
)
,
deg
(
s
)
)
.
(