Refined passport label |
Genus |
Quotient genus |
Group |
Group order |
Dimension |
Signature |
Hyperelliptic |
Cyclic trigonal |
Generating vectors |
2.8-3.0.2-2-2-4.1 |
$2$ |
$0$ |
$D_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
3.8-3.0.2-2-4-4.1 |
$3$ |
$0$ |
$D_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
3.8-3.0.2-2-4-4.2 |
$3$ |
$0$ |
$D_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,5)(2,6)(3,8)(4,7),\ldots$ |
3.8-3.0.2-2-2-2-2.1 |
$3$ |
$0$ |
$D_4$ |
$8$ |
$2$ |
$[ 0; 2, 2, 2, 2, 2 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
3.8-3.1.2.1 |
$3$ |
$1$ |
$D_4$ |
$8$ |
$1$ |
$[ 1; 2 ]$ |
|
|
$(1,5)(2,6)(3,8)(4,7),\ldots$ |
4.8-3.0.2-2-2-2-4.1 |
$4$ |
$0$ |
$D_4$ |
$8$ |
$2$ |
$[ 0; 2, 2, 2, 2, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
4.8-3.0.2-2-2-2-4.3 |
$4$ |
$0$ |
$D_4$ |
$8$ |
$2$ |
$[ 0; 2, 2, 2, 2, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
4.8-3.0.2-2-2-2-4.2 |
$4$ |
$0$ |
$D_4$ |
$8$ |
$2$ |
$[ 0; 2, 2, 2, 2, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
5.8-3.0.2-2-2-4-4.2 |
$5$ |
$0$ |
$D_4$ |
$8$ |
$2$ |
$[ 0; 2, 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
5.8-3.0.2-2-2-4-4.1 |
$5$ |
$0$ |
$D_4$ |
$8$ |
$2$ |
$[ 0; 2, 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
5.8-3.0.2-2-2-2-2-2.3 |
$5$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
5.8-3.0.2-2-2-2-2-2.2 |
$5$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
5.8-3.0.2-2-2-2-2-2.1 |
$5$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
6.8-3.0.2-2-4-4-4.1 |
$6$ |
$0$ |
$D_4$ |
$8$ |
$2$ |
$[ 0; 2, 2, 4, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
6.8-3.0.2-2-2-2-2-4.2 |
$6$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
6.8-3.0.2-2-2-2-2-4.3 |
$6$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
6.8-3.0.2-2-2-2-2-4.1 |
$6$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 2, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
7.8-3.0.2-2-2-2-4-4.5 |
$7$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,5)(2,6)(3,8)(4,7),\ldots$ |
7.8-3.0.2-2-2-2-4-4.2 |
$7$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
7.8-3.0.2-2-2-2-4-4.3 |
$7$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
7.8-3.0.2-2-2-2-4-4.1 |
$7$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
7.8-3.0.2-2-2-2-4-4.4 |
$7$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
7.8-3.0.2-2-2-2-2-2-2.1 |
$7$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
7.8-3.0.2-2-2-2-2-2-2.2 |
$7$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
7.8-3.0.2-2-2-2-2-2-2.3 |
$7$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
8.8-3.0.2-2-2-4-4-4.1 |
$8$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 2, 4, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
8.8-3.0.2-2-2-2-2-2-4.6 |
$8$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
8.8-3.0.2-2-2-2-2-2-4.4 |
$8$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
8.8-3.0.2-2-2-2-2-2-4.3 |
$8$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
8.8-3.0.2-2-2-2-2-2-4.2 |
$8$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
8.8-3.0.2-2-2-2-2-2-4.5 |
$8$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
8.8-3.0.2-2-2-2-2-2-4.1 |
$8$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 2, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
9.8-3.0.2-2-4-4-4-4.2 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 4, 4, 4, 4 ]$ |
|
|
$(1,5)(2,6)(3,8)(4,7),\ldots$ |
9.8-3.0.2-2-4-4-4-4.1 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$3$ |
$[ 0; 2, 2, 4, 4, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
9.8-3.0.2-2-2-2-2-4-4.5 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
9.8-3.0.2-2-2-2-2-4-4.4 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
9.8-3.0.2-2-2-2-2-4-4.3 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
9.8-3.0.2-2-2-2-2-4-4.2 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
9.8-3.0.2-2-2-2-2-4-4.1 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
9.8-3.0.2-2-2-2-2-2-2-2.1 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$5$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
9.8-3.0.2-2-2-2-2-2-2-2.4 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$5$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
9.8-3.0.2-2-2-2-2-2-2-2.6 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$5$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
9.8-3.0.2-2-2-2-2-2-2-2.5 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$5$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
9.8-3.0.2-2-2-2-2-2-2-2.3 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$5$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
9.8-3.0.2-2-2-2-2-2-2-2.2 |
$9$ |
$0$ |
$D_4$ |
$8$ |
$5$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
10.8-3.0.2-2-2-2-4-4-4.3 |
$10$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 4, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
10.8-3.0.2-2-2-2-4-4-4.1 |
$10$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 4, 4, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
10.8-3.0.2-2-2-2-4-4-4.2 |
$10$ |
$0$ |
$D_4$ |
$8$ |
$4$ |
$[ 0; 2, 2, 2, 2, 4, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
10.8-3.0.2-2-2-2-2-2-2-4.5 |
$10$ |
$0$ |
$D_4$ |
$8$ |
$5$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2, 4 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
10.8-3.0.2-2-2-2-2-2-2-4.1 |
$10$ |
$0$ |
$D_4$ |
$8$ |
$5$ |
$[ 0; 2, 2, 2, 2, 2, 2, 2, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |