Family Information
Genus: | $8$ |
Quotient genus: | $0$ |
Group name: | $C_2\times C_6$ |
Group identifier: | $[12,5]$ |
Signature: | $[ 0; 2, 2, 2, 6, 6 ]$ |
Conjugacy classes for this refined passport: | $2, 2, 2, 9, 12$ |
Jacobian variety group algebra decomposition: | $E\times E\times A_{3}\times A_{3}$ |
Corresponding character(s): | $2, 4, 6, 8$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=x^{18}+a_{1}x^{12}+a_{2}x^{6}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
8.12-5.0.2-2-2-6-6.1.1
(1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
(1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
(1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
(1,8,3,7,2,9) (4,11,6,10,5,12) | |
(1,12,2,10,3,11) (4,9,5,7,6,8) |