Properties

Genus \(5\)
Small Group \(A_4:C_4\)
Signature \([ 0; 3, 4, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Group name: $A_4:C_4$
Group identifier: [48,30]
Signature: $[ 0; 3, 4, 4 ]$
Conjugacy classes for this refined passport: 5, 6, 9

Jacobian variety group algebra decomposition:$A_{2}\times E^{3}$
Corresponding character(s): 5, 9

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{12}-33x^8-33x^4+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.48-30.0.3-4-4.1.1

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