Family Information
Genus: | $12$ |
Quotient genus: | $0$ |
Group name: | $Q_{16}$ |
Group identifier: | $[16,9]$ |
Signature: | $[ 0; 2, 2, 4, 4, 8 ]$ |
Conjugacy classes for this refined passport: | $2, 2, 4, 5, 6$ |
Jacobian variety group algebra decomposition: | $A_{12}$ |
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: |
$y^2=x(x^{8}-1)(x^{8}+a_{1}x^{4}+1)(x^{8}+a_{2}x^{4}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
12.16-9.0.2-2-4-4-8.1.1
(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) | |
(1,5,2,6) (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) | |
(1,13,4,16,2,14,3,15) (5,11,8,9,6,12,7,10) |