Properties

Label 6.48-6.0.2-4-24.3
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: $3, 6, 14$

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.

6.48-6.0.2-4-24.3.1

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