Properties

Label 6.48-6.0.2-4-24.4
Genus \(6\)
Quotient genus \(0\)
Group \(C_8:S_3\)
Signature \([ 0; 2, 4, 24 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $6$
Quotient genus: $0$
Group name: $C_8:S_3$
Group identifier: $[48,6]$
Signature: $[ 0; 2, 4, 24 ]$
Conjugacy classes for this refined passport: $3, 6, 15$

Jacobian variety group algebra decomposition:$E^{2}\times A_{2}^{2}$
Corresponding character(s): $8, 12$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24) (25,28) (26,29) (27,30) (31,34) (32,35) (33,36) (37,40) (38,41) (39,42) (43,46) (44,47) (45,48)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{12}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.48-6.0.2-4-24.4.1

  (1,25) (2,27) (3,26) (4,28) (5,30) (6,29) (7,34) (8,36) (9,35) (10,31) (11,33) (12,32) (13,43) (14,45) (15,44) (16,46) (17,48) (18,47) (19,37) (20,39) (21,38) (22,40) (23,42) (24,41)
  (1,42,4,39) (2,41,5,38) (3,40,6,37) (7,45,10,48) (8,44,11,47) (9,43,12,46) (13,27,16,30) (14,26,17,29) (15,25,18,28) (19,36,22,33) (20,35,23,32) (21,34,24,31)
  (1,20,12,13,5,24,7,17,3,19,11,15,4,23,9,16,2,21,10,14,6,22,8,18) (25,44,36,37,29,48,31,41,27,43,35,39,28,47,33,40,26,45,34,38,30,46,32,42)