Family Information
Genus: | $4$ |
Quotient genus: | $0$ |
Group name: | $\SD_{32}$ |
Group identifier: | $[32,19]$ |
Signature: | $[ 0; 2, 4, 16 ]$ |
Conjugacy classes for this refined passport: | $3, 5, 10$ |
Jacobian variety group algebra decomposition: | $A_{2}^{2}$ |
Corresponding character(s): | $8$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=x(x^{8}-1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
4.32-19.0.2-4-16.3.1
(1,9) (2,10) (3,12) (4,11) (5,15) (6,16) (7,13) (8,14) (17,25) (18,26) (19,28) (20,27) (21,31) (22,32) (23,29) (24,30) | |
(1,17,2,18) (3,20,4,19) (5,23,6,24) (7,21,8,22) (9,29,10,30) (11,32,12,31) (13,25,14,26) (15,28,16,27) | |
(1,26,8,31,3,28,5,30,2,25,7,32,4,27,6,29) (9,24,16,19,11,21,13,18,10,23,15,20,12,22,14,17) |