Family Information
Genus: | $9$ |
Quotient genus: | $0$ |
Group name: | $C_2^3$ |
Group identifier: | $[8,5]$ |
Signature: | $[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$ |
Conjugacy classes for this refined passport: | $3, 3, 3, 3, 3, 4, 7, 8$ |
Jacobian variety group algebra decomposition: | $A_{2}\times A_{2}\times A_{2}\times A_{3}$ |
Corresponding character(s): | $2, 4, 6, 8$ |
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: |
$y^2=(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)(x^{4}+a_{3}x^{2}+1)(x^{4}+a_{4}x^{2}+1)(x^{4}+a_{5}x^{2}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
9.8-5.0.2-2-2-2-2-2-2-2.191.1
(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) | |
(1,3) (2,4) (5,7) (6,8) | |
(1,4) (2,3) (5,8) (6,7) | |
(1,7) (2,8) (3,5) (4,6) | |
(1,8) (2,7) (3,6) (4,5) |