Proposition 14.1.
Assuming that:
Φ
⊂
E
(
K
¯
)
be a finite
Gal
(
K
¯
∕
K
)
-stable subgroup
Then
there exists an
elliptic curve
E
′
∕
K
and a separable
isogeny
ϕ
:
E
→
E
′
defined over
K
, with kernel
Φ
, such that every
isogeny
ψ
:
E
→
E
″
with
Φ
⊂
ψ
factors uniquely via
ϕ
:
