Properties

Label 6.48-6.0.2-4-24.1
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: $3, 6, 12$

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.

6.48-6.0.2-4-24.1.1

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