Family Information
Genus: | $6$ |
Quotient genus: | $0$ |
Group name: | $D_{12}$ |
Group identifier: | $[24,6]$ |
Signature: | $[ 0; 2, 2, 3, 4 ]$ |
Conjugacy classes for this refined passport: | $3, 4, 5, 6$ |
Jacobian variety group algebra decomposition: | $E^{2}\times A_{2}^{2}$ |
Corresponding character(s): | $6, 8$ |
Other Data
Hyperelliptic curve(s): | no |
Cyclic trigonal curve(s): | yes |
Trigonal automorphism: | (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) (19,20,21) (22,23,24) |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
6.24-6.0.2-2-3-4.1.1
(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20) | |
(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16) | |
(1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) (19,20,21) (22,23,24) | |
(1,10,4,7) (2,11,5,8) (3,12,6,9) (13,22,16,19) (14,23,17,20) (15,24,18,21) |
6.24-6.0.2-2-3-4.1.2
(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20) | |
(1,20) (2,19) (3,21) (4,23) (5,22) (6,24) (7,14) (8,13) (9,15) (10,17) (11,16) (12,18) | |
(1,3,2) (4,6,5) (7,9,8) (10,12,11) (13,15,14) (16,18,17) (19,21,20) (22,24,23) | |
(1,10,4,7) (2,11,5,8) (3,12,6,9) (13,22,16,19) (14,23,17,20) (15,24,18,21) |
Displaying the unique representative of this refined passport up to braid equivalence.
6.24-6.0.2-2-3-4.1.1
(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20) | |
(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16) | |
(1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) (19,20,21) (22,23,24) | |
(1,10,4,7) (2,11,5,8) (3,12,6,9) (13,22,16,19) (14,23,17,20) (15,24,18,21) |