Families of curves over Q of genus 2 such that G is contained
in the torsion subgroup of the Jacobian.
| Torsion group G |
|G| |
Parameterizing variety |
|
| Z/20Z |
20 |
P2 |
| Z/21Z |
21 |
P2 |
| Z/3Z x Z/9Z |
27 |
P2 |
Z/30Z |
30 |
P2 |
| Z/35Z |
35 |
positive rank elliptic curve |
| Z/6Z x Z/6Z |
36 |
P2 |
| Z/3Z x Z/12Z |
36 |
P2 |
| Z/40Z |
40 |
positive rank elliptic surface |
| Z/45Z |
45 |
positive rank elliptic curve |
| Z/2Z x Z/24Z |
48 |
P2 |
| Z/7Z x Z/7Z |
49 |
P0 |
| Z/5Z x Z/10Z |
50 |
positive rank elliptic surface |
| Z/60Z |
60 |
positive rank elliptic curve |
| Z/63Z |
63 |
P0 |
| Z/8Z x Z/8Z |
64 |
P2 |
| Z/2Z x Z/4Z x Z/8Z |
64 |
P2 |
| Z/6Z x Z/12Z |
72 |
positive rank elliptic surface |
| Z/2Z x Z/6Z x Z/6Z |
72 |
positive rank elliptic surface |
| Z/2Z x Z/2Z x Z/24Z |
96 |
positive rank elliptic curve |
| Z/2Z x Z/2Z x Z/4Z x Z/8Z |
128 |
positive rank elliptic surface |