Family Information
Genus: | $14$ |
Quotient genus: | $0$ |
Group name: | $C_3:D_4$ |
Group identifier: | $[24,8]$ |
Signature: | $[ 0; 2, 2, 2, 4, 6 ]$ |
Conjugacy classes for this refined passport: | $2, 2, 4, 6, 9$ |
Jacobian variety group algebra decomposition: | $A_{2}^{2}\times A_{5}^{2}$ |
Corresponding character(s): | $7, 8$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=(x^{6}-1)(x^{12}+a_{1}x^{6}+1)(x^{12}+a_{2}x^{6}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
14.24-8.0.2-2-2-4-6.2.1
(1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24) | |
(1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24) | |
(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20) | |
(1,20,4,23) (2,19,5,22) (3,21,6,24) (7,17,10,14) (8,16,11,13) (9,18,12,15) | |
(1,9,2,7,3,8) (4,12,5,10,6,11) (13,21,14,19,15,20) (16,24,17,22,18,23) |