Family Information
Genus: | $12$ |
Quotient genus: | $0$ |
Group name: | $\SL(2,3)$ |
Group identifier: | $[24,3]$ |
Signature: | $[ 0; 2, 4, 6, 6 ]$ |
Conjugacy classes for this refined passport: | $2, 5, 6, 7$ |
Jacobian variety group algebra decomposition: | $A_{4}\times A_{4}^{2}$ |
Corresponding character(s): | $4, 5$ |
Other Data
Hyperelliptic curve(s): | yes |
Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) |
Cyclic trigonal curve(s): | no |
Equation(s) of curve(s) in this refined passport: |
$y^2=x(x^4-1)(x^8+14x^4+1)(x^{12}-a_{1}x^{10}-33x^8+2a_{1}x^6-33x^4-a_{1}x^2+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
12.24-3.0.2-4-6-6.1.1
(1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) | |
(1,3,2,4) (5,7,6,8) (9,11,10,12) (13,15,14,16) (17,19,18,20) (21,23,22,24) | |
(1,16,20,2,15,19) (3,9,24,4,10,23) (5,14,21,6,13,22) (7,11,17,8,12,18) | |
(1,18,9,2,17,10) (3,22,15,4,21,16) (5,24,11,6,23,12) (7,20,13,8,19,14) |