Family Information
Genus: | $3$ |
Quotient genus: | $0$ |
Group name: | $D_4:C_4$ |
Group identifier: | $[32,9]$ |
Signature: | $[ 0; 2, 4, 8 ]$ |
Conjugacy classes for this refined passport: | $5, 10, 13$ |
Jacobian variety group algebra decomposition: | $E\times E^{2}$ |
Corresponding character(s): | $6, 12$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) (13,15) (14,16) (17,19) (18,20) (21,23) (22,24) (25,27) (26,28) (29,31) (30,32) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=x^{8}-1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
3.32-9.0.2-4-8.4.1
(1,9) (2,10) (3,11) (4,12) (5,14) (6,13) (7,16) (8,15) (17,25) (18,26) (19,27) (20,28) (21,30) (22,29) (23,32) (24,31) | |
(1,20,3,18) (2,19,4,17) (5,23,7,21) (6,24,8,22) (9,32,11,30) (10,31,12,29) (13,28,15,26) (14,27,16,25) | |
(1,26,8,31,2,25,7,32) (3,28,6,29,4,27,5,30) (9,21,16,19,10,22,15,20) (11,23,14,17,12,24,13,18) |