Family Information
Genus: | $5$ |
Quotient genus: | $0$ |
Group name: | $C_2^2:C_4$ |
Group identifier: | $[16,3]$ |
Signature: | $[ 0; 2, 2, 4, 4 ]$ |
Conjugacy classes for this refined passport: | $2, 6, 8, 9$ |
Jacobian variety group algebra decomposition: | $A_{2}\times E\times E^{2}$ |
Corresponding character(s): | $5, 6, 9$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=(x^{4}-1)(x^{8}+a_{1}x^{4}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.16-3.0.2-2-4-4.4.1
(1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) | |
(1,6) (2,5) (3,8) (4,7) (9,14) (10,13) (11,16) (12,15) | |
(1,10,2,9) (3,12,4,11) (5,16,6,15) (7,14,8,13) | |
(1,13,4,16) (2,14,3,15) (5,11,8,10) (6,12,7,9) |