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: | $3, 3, 3, 8, 11$ |
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: | (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) |
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.
8.12-5.0.2-2-2-6-6.15.1
(1,7) (2,8) (3,9) (4,10) (5,11) (6,12) | |
(1,7) (2,8) (3,9) (4,10) (5,11) (6,12) | |
(1,7) (2,8) (3,9) (4,10) (5,11) (6,12) | |
(1,6,2,4,3,5) (7,12,8,10,9,11) | |
(1,11,3,10,2,12) (4,8,6,7,5,9) |