Torsion group of y
2
=x(x
2
+a)
type 1 : P
1
(0,0) for all
type 2 : a=4, P
n
(2,±4)
type 3 : a=-c
2
, P
n
(±c,0)
type 1 : P
1
(0,0)
for all :
Z/2Z
P
1
O
P
1
(0,0)
O
P
1
O
P
1
O
type 2 : a=4, P
n
(2,±4)
:
Z/4Z
P
1
P
2
P
3
O
P
1
(2,-4)
P
3
O
P
2
P
1
P
2
(2,4)
O
P
3
P
1
P
2
P
3
(0,0)
P
2
P
1
O
P
3
O
P
1
P
2
P
3
O
type 3 : a=-c
2
, P
n
(±c,0) :
Z/4Z
P
1
P
2
P
3
O
P
1
(c,0)
O
P
3
P
2
P
1
P
2
(-c,0)
P
3
O
P
1
P
2
P
3
(0,0)
P
2
P
1
O
P
3
O
P
1
P
2
P
3
O
table of curves (English)
E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima