Torsion group G | |G| | Parameterizing variety | All hyperelliptic? |
---|---|---|---|
Z/2Z x Z/30Z | 60 | positive rank elliptic curve | yes |
Z/10Z x Z/10Z | 100 | P1 | yes |
Z/2Z x Z/8Z x Z/8Z | 128 | positive rank elliptic surface | yes |
Z/4Z x Z/4Z x Z/8Z | 128 | P1 | yes |
Z/4Z x Z/40Z | 160 | positive rank elliptic curve | no |
Z/2Z x Z/4Z x Z/24Z | 192 | positive rank elliptic curve | no |
Z/2Z x Z/2Z x Z/2Z x Z/24Z | 192 | positive rank elliptic surface | yes |
Z/10Z x Z/20Z | 200 | P2 | no |
Z/6Z x Z/6Z x Z/6Z | 216 | positive rank elliptic curve | no |
Z/4Z x Z/60Z | 240 | positive rank elliptic curve | no |
Z/4Z x Z/8Z x Z/8Z | 256 | positive rank elliptic curve | no |
Z/2Z x Z/2Z x Z/8Z x Z/8Z | 256 | P2 | no |
Z/2Z x Z/4Z x Z/4Z x Z/8Z | 256 | P2 | no |
Z/2Z x Z/2Z x Z/2Z x Z/4Z x Z/8Z | 256 | P2 | yes |
Z/2Z x Z/12Z x Z/12Z | 288 | P2 | no |
Z/2Z x Z/2Z x Z/6Z x Z/12Z | 288 | positive rank elliptic surface | yes |
Z/2Z x Z/2Z x Z/4Z x Z/4Z x Z/8Z | 512 | positive rank elliptic curve | no |
Z/2Z x Z/2Z x Z/2Z x Z/2Z x Z/4Z x Z/8Z | 512 | P1 | yes |
Z/6Z x Z/12Z x Z/12Z | 864 | P0 | no |