Properties

Label 8.48-25.0.2-6-24.3
Genus \(8\)
Quotient genus \(0\)
Group \(C_3\times D_8\)
Signature \([ 0; 2, 6, 24 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $8$
Quotient genus: $0$
Group name: $C_3\times D_8$
Group identifier: $[48,25]$
Signature: $[ 0; 2, 6, 24 ]$
Conjugacy classes for this refined passport: $3, 13, 18$

Jacobian variety group algebra decomposition:$E\times E\times E^{2}\times A_{2}^{2}$
Corresponding character(s): $5, 6, 14, 18$

Other Data

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

8.48-25.0.2-6-24.3.1

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