Family Information
Genus: | $3$ |
Quotient genus: | $0$ |
Group name: | $C_2\times D_4$ |
Group identifier: | $[16,11]$ |
Signature: | $[ 0; 2, 2, 2, 4 ]$ |
Conjugacy classes for this refined passport: | $4, 5, 7, 10$ |
Jacobian variety group algebra decomposition: | $E\times E^{2}$ |
Corresponding character(s): | $6, 9$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) (13,16) (14,15) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=x^{8}+a_1x^{4}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
3.16-11.0.2-2-2-4.5.1
(1,4) (2,3) (5,8) (6,7) (9,12) (10,11) (13,16) (14,15) | |
(1,5) (2,6) (3,7) (4,8) (9,13) (10,14) (11,15) (12,16) | |
(1,9) (2,10) (3,11) (4,12) (5,14) (6,13) (7,16) (8,15) | |
(1,16,2,15) (3,14,4,13) (5,11,6,12) (7,9,8,10) |