Family Information
Genus: | $9$ |
Quotient genus: | $0$ |
Group name: | $C_2\times C_4$ |
Group identifier: | $[8,2]$ |
Signature: | $[ 0; 2, 2, 2, 2, 2, 4, 4 ]$ |
Conjugacy classes for this refined passport: | $4, 4, 4, 4, 4, 6, 8$ |
Jacobian variety group algebra decomposition: | $A_{2}\times A_{5}\times A_{2}$ |
Corresponding character(s): | $2, 4, 6$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,4) (2,3) (5,8) (6,7) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=x^{20}+a_{1}x^{16}+a_{2}x^{12}+a_{3}x^{8}+a_{4}x^{4}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
9.8-2.0.2-2-2-2-2-4-4.50.1
(1,4) (2,3) (5,8) (6,7) | |
(1,4) (2,3) (5,8) (6,7) | |
(1,4) (2,3) (5,8) (6,7) | |
(1,4) (2,3) (5,8) (6,7) | |
(1,4) (2,3) (5,8) (6,7) | |
(1,6,2,5) (3,8,4,7) | |
(1,8,2,7) (3,6,4,5) |