Family Information
Genus: | $5$ |
Quotient genus: | $0$ |
Group name: | $C_2\times C_4$ |
Group identifier: | $[8,2]$ |
Signature: | $[ 0; 2, 2, 2, 4, 4 ]$ |
Conjugacy classes for this refined passport: | $3, 3, 3, 6, 7$ |
Jacobian variety group algebra decomposition: | $E\times A_{3}\times E$ |
Corresponding character(s): | $2, 4, 6$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,3) (2,4) (5,7) (6,8) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=x^{12}+a_{1}x^{8}+a_{2}x^{4}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.8-2.0.2-2-2-4-4.16.1
(1,3) (2,4) (5,7) (6,8) | |
(1,3) (2,4) (5,7) (6,8) | |
(1,3) (2,4) (5,7) (6,8) | |
(1,6,2,5) (3,8,4,7) | |
(1,7,2,8) (3,5,4,6) |