Family Information
| Genus: | $14$ |
| Quotient genus: | $0$ |
| Group name: | $D_{21}$ |
| Group identifier: | $[42,5]$ |
| Signature: | $[ 0; 2, 2, 3, 21 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 3, 7$ |
| Jacobian variety group algebra decomposition: | $E^{2}\times A_{6}^{2}$ |
| Corresponding character(s): | $3, 7$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | yes |
| Trigonal automorphism: | (1,8,15) (2,9,16) (3,10,17) (4,11,18) (5,12,19) (6,13,20) (7,14,21) (22,29,36) (23,30,37) (24,31,38) (25,32,39) (26,33,40) (27,34,41) (28,35,42) |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
14.42-5.0.2-2-3-21.1.1
| (1,22) (2,28) (3,27) (4,26) (5,25) (6,24) (7,23) (8,36) (9,42) (10,41) (11,40) (12,39) (13,38) (14,37) (15,29) (16,35) (17,34) (18,33) (19,32) (20,31) (21,30) | |
| (1,28) (2,27) (3,26) (4,25) (5,24) (6,23) (7,22) (8,42) (9,41) (10,40) (11,39) (12,38) (13,37) (14,36) (15,35) (16,34) (17,33) (18,32) (19,31) (20,30) (21,29) | |
| (1,15,8) (2,16,9) (3,17,10) (4,18,11) (5,19,12) (6,20,13) (7,21,14) (22,36,29) (23,37,30) (24,38,31) (25,39,32) (26,40,33) (27,41,34) (28,42,35) | |
| (1,9,17,4,12,20,7,8,16,3,11,19,6,14,15,2,10,18,5,13,21) (22,30,38,25,33,41,28,29,37,24,32,40,27,35,36,23,31,39,26,34,42) |
14.42-5.0.2-2-3-21.1.2
| (1,22) (2,28) (3,27) (4,26) (5,25) (6,24) (7,23) (8,36) (9,42) (10,41) (11,40) (12,39) (13,38) (14,37) (15,29) (16,35) (17,34) (18,33) (19,32) (20,31) (21,30) | |
| (1,37) (2,36) (3,42) (4,41) (5,40) (6,39) (7,38) (8,30) (9,29) (10,35) (11,34) (12,33) (13,32) (14,31) (15,23) (16,22) (17,28) (18,27) (19,26) (20,25) (21,24) | |
| (1,15,8) (2,16,9) (3,17,10) (4,18,11) (5,19,12) (6,20,13) (7,21,14) (22,36,29) (23,37,30) (24,38,31) (25,39,32) (26,40,33) (27,41,34) (28,42,35) | |
| (1,21,13,5,18,10,2,15,14,6,19,11,3,16,8,7,20,12,4,17,9) (22,42,34,26,39,31,23,36,35,27,40,32,24,37,29,28,41,33,25,38,30) |