Refined passport label |
Genus |
Quotient genus |
Group |
Group order |
Dimension |
Signature |
Hyperelliptic |
Cyclic trigonal |
Generating vectors |
2.12-4.0.2-2-2-3.1 |
$2$ |
$0$ |
$D_6$ |
$12$ |
$1$ |
$[ 0; 2, 2, 2, 3 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
3.12-4.0.2-2-2-6.2 |
$3$ |
$0$ |
$D_6$ |
$12$ |
$1$ |
$[ 0; 2, 2, 2, 6 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
3.12-4.0.2-2-2-6.1 |
$3$ |
$0$ |
$D_6$ |
$12$ |
$1$ |
$[ 0; 2, 2, 2, 6 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
4.12-4.0.2-2-3-6.1 |
$4$ |
$0$ |
$D_6$ |
$12$ |
$1$ |
$[ 0; 2, 2, 3, 6 ]$ |
|
✓ |
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
4.12-4.0.2-2-2-2-2.1 |
$4$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
4.12-4.0.2-2-2-2-2.2 |
$4$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
5.12-4.0.2-2-6-6.2 |
$5$ |
$0$ |
$D_6$ |
$12$ |
$1$ |
$[ 0; 2, 2, 6, 6 ]$ |
|
|
$(1,10)(2,12)(3,11)(4,7)(5,9)(6,8),\ldots$ |
5.12-4.0.2-2-6-6.1 |
$5$ |
$0$ |
$D_6$ |
$12$ |
$1$ |
$[ 0; 2, 2, 6, 6 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
5.12-4.0.2-2-2-2-3.2 |
$5$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 2, 3 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
5.12-4.0.2-2-2-2-3.3 |
$5$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 2, 3 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
5.12-4.0.2-2-2-2-3.1 |
$5$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 2, 3 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
6.12-4.0.2-2-2-3-3.1 |
$6$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 3, 3 ]$ |
|
✓ |
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
6.12-4.0.2-2-2-2-6.3 |
$6$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 2, 6 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
6.12-4.0.2-2-2-2-6.1 |
$6$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 2, 6 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
6.12-4.0.2-2-2-2-6.2 |
$6$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 2, 6 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
7.12-4.0.2-2-2-3-6.2 |
$7$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 3, 6 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
7.12-4.0.2-2-2-3-6.1 |
$7$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 3, 6 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
7.12-4.0.2-2-2-2-2-2.1 |
$7$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
7.12-4.0.2-2-2-2-2-2.5 |
$7$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
7.12-4.0.2-2-2-2-2-2.4 |
$7$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
7.12-4.0.2-2-2-2-2-2.3 |
$7$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
7.12-4.0.2-2-2-2-2-2.2 |
$7$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
8.12-4.0.2-2-2-6-6.1 |
$8$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 2, 6, 6 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
8.12-4.0.2-2-3-3-6.1 |
$8$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 3, 3, 6 ]$ |
|
✓ |
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
8.12-4.0.2-2-2-2-2-3.1 |
$8$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 3 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
8.12-4.0.2-2-2-2-2-3.3 |
$8$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 3 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
8.12-4.0.2-2-2-2-2-3.2 |
$8$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 3 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
9.12-4.0.2-2-3-6-6.2 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 3, 6, 6 ]$ |
|
|
$(1,10)(2,12)(3,11)(4,7)(5,9)(6,8),\ldots$ |
9.12-4.0.2-2-3-6-6.1 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 3, 6, 6 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
9.12-4.0.2-2-2-2-2-6.5 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 6 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
9.12-4.0.2-2-2-2-2-6.4 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 6 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
9.12-4.0.2-2-2-2-2-6.3 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 6 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
9.12-4.0.2-2-2-2-3-3.3 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 3, 3 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
9.12-4.0.2-2-2-2-3-3.2 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 3, 3 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
9.12-4.0.2-2-2-2-3-3.1 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 3, 3 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
9.12-4.0.2-2-2-2-2-6.2 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 6 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
9.12-4.0.2-2-2-2-2-6.1 |
$9$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 6 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
10.12-4.0.2-2-6-6-6.1 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$2$ |
$[ 0; 2, 2, 6, 6, 6 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
10.12-4.0.2-2-2-2-3-6.1 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 3, 6 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
10.12-4.0.2-2-2-3-3-3.1 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 3, 3, 3 ]$ |
|
✓ |
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
10.12-4.0.2-2-2-2-3-6.3 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 3, 6 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
10.12-4.0.2-2-2-2-3-6.2 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 3, 6 ]$ |
|
|
$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$ |
10.12-4.0.2-2-2-2-2-2-2.4 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
10.12-4.0.2-2-2-2-2-2-2.3 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
10.12-4.0.2-2-2-2-2-2-2.2 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
10.12-4.0.2-2-2-2-2-2-2.1 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
10.12-4.0.2-2-2-2-2-2-2.5 |
$10$ |
$0$ |
$D_6$ |
$12$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
11.12-4.0.2-2-2-2-6-6.5 |
$11$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 2, 6, 6 ]$ |
|
|
$(1,10)(2,12)(3,11)(4,7)(5,9)(6,8),\ldots$ |
11.12-4.0.2-2-2-3-3-6.2 |
$11$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 3, 3, 6 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
11.12-4.0.2-2-2-3-3-6.1 |
$11$ |
$0$ |
$D_6$ |
$12$ |
$3$ |
$[ 0; 2, 2, 2, 3, 3, 6 ]$ |
|
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |