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: | $2, 3, 5, 8, 8, 8, 8, 8$ |
Jacobian variety group algebra decomposition: | $A_{2}\times A_{2}\times A_{2}\times A_{3}$ |
Corresponding character(s): | $2, 3, 5, 8$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,8) (2,7) (3,6) (4,5) |
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.
9.8-5.0.2-2-2-2-2-2-2-2.153.1
(1,2) (3,4) (5,6) (7,8) | |
(1,3) (2,4) (5,7) (6,8) | |
(1,5) (2,6) (3,7) (4,8) | |
(1,8) (2,7) (3,6) (4,5) | |
(1,8) (2,7) (3,6) (4,5) | |
(1,8) (2,7) (3,6) (4,5) | |
(1,8) (2,7) (3,6) (4,5) | |
(1,8) (2,7) (3,6) (4,5) |