Family Information
Genus: | $12$ |
Quotient genus: | $0$ |
Group name: | $\SD_{32}$ |
Group identifier: | $[32,19]$ |
Signature: | $[ 0; 2, 2, 4, 16 ]$ |
Conjugacy classes for this refined passport: | $2, 3, 5, 11$ |
Jacobian variety group algebra decomposition: | $A_{6}^{2}$ |
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: |
$y^2=x(x^{8}-1)(x^{16}+a_{1}x^{8}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
12.32-19.0.2-2-4-16.4.1
(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) | |
(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) | |
(1,19,2,20) (3,17,4,18) (5,22,6,21) (7,23,8,24) (9,31,10,32) (11,29,12,30) (13,27,14,28) (15,25,16,26) | |
(1,28,7,29,3,25,6,31,2,27,8,30,4,26,5,32) (9,21,15,17,11,23,14,19,10,22,16,18,12,24,13,20) |