Family Information
Genus: | $10$ |
Quotient genus: | $0$ |
Group name: | $\SL(2,3)$ |
Group identifier: | $[24,3]$ |
Signature: | $[ 0; 2, 3, 4, 6 ]$ |
Conjugacy classes for this refined passport: | $2, 4, 5, 6$ |
Jacobian variety group algebra decomposition: | $A_{4}\times A_{3}^{2}$ |
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: |
$y^2=x(x^4-1)(x^4+2i\\sqrt{3}x^2+1)(x^{12}-a_{1}x^{10}-33x^8+2a_{1}x^6-33x^4-a_{1}x^2+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
10.24-3.0.2-3-4-6.2.1
(1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) | |
(1,17,9) (2,18,10) (3,21,15) (4,22,16) (5,23,11) (6,24,12) (7,19,13) (8,20,14) | |
(1,4,2,3) (5,8,6,7) (9,12,10,11) (13,16,14,15) (17,20,18,19) (21,24,22,23) | |
(1,16,20,2,15,19) (3,9,24,4,10,23) (5,14,21,6,13,22) (7,11,17,8,12,18) |