Refined passport label |
Genus |
Quotient genus |
Group |
Group order |
Dimension |
Signature |
Hyperelliptic |
Cyclic trigonal |
Generating vectors |
2.3-1.0.3-3-3-3.1 |
$2$ |
$0$ |
$C_3$ |
$3$ |
$1$ |
$[ 0; 3, 3, 3, 3 ]$ |
|
|
$(1,2,3),\ldots$ |
2.4-1.0.2-2-4-4.1 |
$2$ |
$0$ |
$C_4$ |
$4$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,2)(3,4),\ldots$ |
2.6-1.0.2-2-3-3.1 |
$2$ |
$0$ |
$S_3$ |
$6$ |
$1$ |
$[ 0; 2, 2, 3, 3 ]$ |
|
|
$(1,4)(2,6)(3,5),\ldots$ |
2.6-2.0.2-2-3-3.1 |
$2$ |
$0$ |
$C_6$ |
$6$ |
$1$ |
$[ 0; 2, 2, 3, 3 ]$ |
|
|
$(1,4)(2,5)(3,6),\ldots$ |
2.8-3.0.2-2-2-4.1 |
$2$ |
$0$ |
$D_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
2.12-4.0.2-2-2-3.1 |
$2$ |
$0$ |
$D_6$ |
$12$ |
$1$ |
$[ 0; 2, 2, 2, 3 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
3.4-1.0.4-4-4-4.3 |
$3$ |
$0$ |
$C_4$ |
$4$ |
$1$ |
$[ 0; 4, 4, 4, 4 ]$ |
|
|
$(1,4,2,3),\ldots$ |
3.4-1.0.4-4-4-4.1 |
$3$ |
$0$ |
$C_4$ |
$4$ |
$1$ |
$[ 0; 4, 4, 4, 4 ]$ |
|
|
$(1,3,2,4),\ldots$ |
3.4-1.0.4-4-4-4.2 |
$3$ |
$0$ |
$C_4$ |
$4$ |
$1$ |
$[ 0; 4, 4, 4, 4 ]$ |
|
|
$(1,3,2,4),\ldots$ |
3.6-2.0.2-3-3-6.1 |
$3$ |
$0$ |
$C_6$ |
$6$ |
$1$ |
$[ 0; 2, 3, 3, 6 ]$ |
|
✓ |
$(1,4)(2,5)(3,6),\ldots$ |
3.6-2.0.2-3-3-6.2 |
$3$ |
$0$ |
$C_6$ |
$6$ |
$1$ |
$[ 0; 2, 3, 3, 6 ]$ |
|
✓ |
$(1,4)(2,5)(3,6),\ldots$ |
3.6-2.0.2-2-6-6.1 |
$3$ |
$0$ |
$C_6$ |
$6$ |
$1$ |
$[ 0; 2, 2, 6, 6 ]$ |
|
|
$(1,4)(2,5)(3,6),\ldots$ |
3.6-1.1.3.1 |
$3$ |
$1$ |
$S_3$ |
$6$ |
$1$ |
$[ 1; 3 ]$ |
|
|
$(1,4)(2,6)(3,5),\ldots$ |
3.8-2.0.2-2-4-4.10 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
3.8-2.0.2-2-4-4.9 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
3.8-2.0.2-2-4-4.5 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
3.8-2.0.2-2-4-4.8 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
3.8-2.0.2-2-4-4.7 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
3.8-3.0.2-2-4-4.1 |
$3$ |
$0$ |
$D_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
3.8-2.0.2-2-4-4.1 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
3.8-2.0.2-2-4-4.4 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
3.8-3.0.2-2-4-4.2 |
$3$ |
$0$ |
$D_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,5)(2,6)(3,8)(4,7),\ldots$ |
3.8-2.0.2-2-4-4.11 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,4)(2,3)(5,8)(6,7),\ldots$ |
3.8-2.0.2-2-4-4.2 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
3.8-2.0.2-2-4-4.6 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,3)(2,4)(5,7)(6,8),\ldots$ |
3.8-2.0.2-2-4-4.12 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
|
|
$(1,4)(2,3)(5,8)(6,7),\ldots$ |
3.8-2.0.2-2-4-4.3 |
$3$ |
$0$ |
$C_2\times C_4$ |
$8$ |
$1$ |
$[ 0; 2, 2, 4, 4 ]$ |
✓ |
|
$(1,2)(3,4)(5,6)(7,8),\ldots$ |
3.8-4.1.2.1 |
$3$ |
$1$ |
$Q_8$ |
$8$ |
$1$ |
$[ 1; 2 ]$ |
|
|
$(1,5,2,6)(3,8,4,7),\ldots$ |
3.8-3.1.2.1 |
$3$ |
$1$ |
$D_4$ |
$8$ |
$1$ |
$[ 1; 2 ]$ |
|
|
$(1,5)(2,6)(3,8)(4,7),\ldots$ |
3.12-3.0.2-2-3-3.1 |
$3$ |
$0$ |
$A_4$ |
$12$ |
$1$ |
$[ 0; 2, 2, 3, 3 ]$ |
|
|
$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$ |
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 |
$3$ |
$0$ |
$D_6$ |
$12$ |
$1$ |
$[ 0; 2, 2, 2, 6 ]$ |
✓ |
|
$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$ |
3.16-11.0.2-2-2-4.1 |
$3$ |
$0$ |
$C_2\times D_4$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$ |
3.16-11.0.2-2-2-4.5 |
$3$ |
$0$ |
$C_2\times D_4$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$ |
3.16-11.0.2-2-2-4.4 |
$3$ |
$0$ |
$C_2\times D_4$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$ |
3.16-11.0.2-2-2-4.2 |
$3$ |
$0$ |
$C_2\times D_4$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$ |
3.16-11.0.2-2-2-4.6 |
$3$ |
$0$ |
$C_2\times D_4$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$ |
3.16-11.0.2-2-2-4.7 |
$3$ |
$0$ |
$C_2\times D_4$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$ |
3.16-13.0.2-2-2-4.2 |
$3$ |
$0$ |
$D_4:C_2$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
|
|
$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$ |
3.16-11.0.2-2-2-4.3 |
$3$ |
$0$ |
$C_2\times D_4$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$ |
3.16-11.0.2-2-2-4.8 |
$3$ |
$0$ |
$C_2\times D_4$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
✓ |
|
$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$ |
3.16-13.0.2-2-2-4.1 |
$3$ |
$0$ |
$D_4:C_2$ |
$16$ |
$1$ |
$[ 0; 2, 2, 2, 4 ]$ |
|
|
$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$ |
3.24-12.0.2-2-2-3.1 |
$3$ |
$0$ |
$S_4$ |
$24$ |
$1$ |
$[ 0; 2, 2, 2, 3 ]$ |
|
|
$(1,2)\cdots(23,24),\ldots$ |
4.5-1.0.5-5-5-5.5 |
$4$ |
$0$ |
$C_5$ |
$5$ |
$1$ |
$[ 0; 5, 5, 5, 5 ]$ |
|
|
$(1,3,5,2,4),\ldots$ |
4.5-1.0.5-5-5-5.7 |
$4$ |
$0$ |
$C_5$ |
$5$ |
$1$ |
$[ 0; 5, 5, 5, 5 ]$ |
|
|
$(1,4,2,5,3),\ldots$ |
4.5-1.0.5-5-5-5.1 |
$4$ |
$0$ |
$C_5$ |
$5$ |
$1$ |
$[ 0; 5, 5, 5, 5 ]$ |
|
|
$(1,2,3,4,5),\ldots$ |
4.5-1.0.5-5-5-5.2 |
$4$ |
$0$ |
$C_5$ |
$5$ |
$1$ |
$[ 0; 5, 5, 5, 5 ]$ |
|
|
$(1,2,3,4,5),\ldots$ |
4.5-1.0.5-5-5-5.3 |
$4$ |
$0$ |
$C_5$ |
$5$ |
$1$ |
$[ 0; 5, 5, 5, 5 ]$ |
|
|
$(1,2,3,4,5),\ldots$ |
4.5-1.0.5-5-5-5.4 |
$4$ |
$0$ |
$C_5$ |
$5$ |
$1$ |
$[ 0; 5, 5, 5, 5 ]$ |
|
|
$(1,2,3,4,5),\ldots$ |
4.5-1.0.5-5-5-5.6 |
$4$ |
$0$ |
$C_5$ |
$5$ |
$1$ |
$[ 0; 5, 5, 5, 5 ]$ |
|
|
$(1,3,5,2,4),\ldots$ |