Family Information
Genus: | $12$ |
Quotient genus: | $0$ |
Group name: | $D_8$ |
Group identifier: | $[16,7]$ |
Signature: | $[ 0; 2, 2, 2, 2, 2, 8 ]$ |
Conjugacy classes for this refined passport: | $2, 2, 2, 3, 4, 7$ |
Jacobian variety group algebra decomposition: | $A_{6}^{2}$ |
Corresponding character(s): | $6$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=x(x^{8}+a_{1}x^{4}+1)(x^{8}+a_{2}x^{4}+1)(x^{8}+a_{3}x^{4}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
12.16-7.0.2-2-2-2-2-8.2.1
(1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) | |
(1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) | |
(1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) | |
(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15) | |
(1,9) (2,10) (3,12) (4,11) (5,15) (6,16) (7,13) (8,14) | |
(1,14,4,15,2,13,3,16) (5,11,8,9,6,12,7,10) |