Family Information
Genus: | $6$ |
Quotient genus: | $0$ |
Group name: | $Q_8$ |
Group identifier: | $[8,4]$ |
Signature: | $[ 0; 2, 2, 4, 4, 4 ]$ |
Conjugacy classes for this refined passport: | $2, 2, 3, 4, 5$ |
Jacobian variety group algebra decomposition: | $A_{6}$ |
Corresponding character(s): | $5$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=x(x^{4}-1)(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
6.8-4.0.2-2-4-4-4.1.1
(1,2) (3,4) (5,6) (7,8) | |
(1,2) (3,4) (5,6) (7,8) | |
(1,3,2,4) (5,7,6,8) | |
(1,5,2,6) (3,8,4,7) | |
(1,7,2,8) (3,5,4,6) |