Family Information
Genus: | $4$ |
Quotient genus: | $0$ |
Group name: | $C_6\times S_3$ |
Group identifier: | $[36,12]$ |
Signature: | $[ 0; 2, 6, 6 ]$ |
Conjugacy classes for this refined passport: | $4, 14, 15$ |
Jacobian variety group algebra decomposition: | $E\times E\times E^{2}$ |
Corresponding character(s): | $6, 7, 16$ |
Other Data
Hyperelliptic curve(s): | no |
Cyclic trigonal curve(s): | yes |
Trigonal automorphism: | (1,4,7) (2,5,8) (3,6,9) (10,13,16) (11,14,17) (12,15,18) (19,22,25) (20,23,26) (21,24,27) (28,31,34) (29,32,35) (30,33,36) |
Equation(s) of curve(s) in this refined passport: |
$y^3 = (x^3-1)(x^3 + 1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
4.36-12.0.2-6-6.4.1
(1,28) (2,30) (3,29) (4,31) (5,33) (6,32) (7,34) (8,36) (9,35) (10,19) (11,21) (12,20) (13,22) (14,24) (15,23) (16,25) (17,27) (18,26) | |
(1,18,5,10,9,14) (2,16,6,11,7,15) (3,17,4,12,8,13) (19,36,23,28,27,32) (20,34,24,29,25,33) (21,35,22,30,26,31) | |
(1,24,7,21,4,27) (2,23,8,20,5,26) (3,22,9,19,6,25) (10,33,16,30,13,36) (11,32,17,29,14,35) (12,31,18,28,15,34) |