Family Information
Genus: | $7$ |
Quotient genus: | $0$ |
Group name: | $C_2\times C_4$ |
Group identifier: | $[8,2]$ |
Signature: | $[ 0; 2, 2, 2, 2, 4, 4 ]$ |
Conjugacy classes for this refined passport: | $3, 3, 3, 3, 7, 8$ |
Jacobian variety group algebra decomposition: | $E\times A_{4}\times A_{2}$ |
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: |
$y^2=x^{16}+a_{1}x^{12}+a_{2}x^{8}+a_{3}x^{4}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
7.8-2.0.2-2-2-2-4-4.22.1
(1,3) (2,4) (5,7) (6,8) | |
(1,3) (2,4) (5,7) (6,8) | |
(1,3) (2,4) (5,7) (6,8) | |
(1,3) (2,4) (5,7) (6,8) | |
(1,7,2,8) (3,5,4,6) | |
(1,8,2,7) (3,6,4,5) |