Theorem 10.5
(Lutz Nagell)
.
Assuming that:
E
∕
ℚ
:
y
2
=
x
3
+
a
x
+
b
,
a
,
b
∈
ℤ
0
≠
T
=
(
x
,
y
)
∈
E
(
ℚ
)
tors
Then
x
,
y
∈
ℤ
and either
y
=
0
or
y
2
|
(
4
a
3
+
2
7
b
2
)
.