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: | $3, 5, 8$ |
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.
4.32-19.0.2-4-16.1.1
(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) | |
(1,18,2,17) (3,19,4,20) (5,24,6,23) (7,22,8,21) (9,30,10,29) (11,31,12,32) (13,26,14,25) (15,27,16,28) | |
(1,25,8,32,3,27,5,29,2,26,7,31,4,28,6,30) (9,23,16,20,11,22,13,17,10,24,15,19,12,21,14,18) |