Family Information
Genus: | $14$ |
Quotient genus: | $0$ |
Group name: | $C_3:C_4$ |
Group identifier: | $[12,1]$ |
Signature: | $[ 0; 2, 2, 2, 2, 3, 4, 4 ]$ |
Conjugacy classes for this refined passport: | $2, 2, 2, 2, 3, 4, 5$ |
Jacobian variety group algebra decomposition: | $A_{4}\times A_{10}$ |
Corresponding character(s): | $3, 5$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=(x^{6}-1)(x^{6}+a_{1}x^{3}+1)(x^{6}+a_{2}x^{3}+1)(x^{6}+a_{3}x^{3}+1)(x^{6}+a_{4}x^{3}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
14.12-1.0.2-2-2-2-3-4-4.1.1
(1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
(1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
(1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
(1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
(1,2,3) (4,5,6) (7,8,9) (10,11,12) | |
(1,7,4,10) (2,9,5,12) (3,8,6,11) | |
(1,12,4,9) (2,11,5,8) (3,10,6,7) |