Properties

Genus \(5\)
Small Group \(C_3\times D_5\)
Signature \([ 0; 2, 6, 15 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Group name: $C_3\times D_5$
Group identifier: [30,2]
Signature: $[ 0; 2, 6, 15 ]$
Conjugacy classes for this refined passport: 2, 7, 10

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

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):Yes
Trigonal automorphism: (1,6,11) (2,7,12) (3,8,13) (4,9,14) (5,10,15) (16,21,26) (17,22,27) (18,23,28) (19,24,29) (20,25,30)

Equation(s) of curve(s) in this refined passport:
  $y^3=(x^5-1)x^2$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.30-2.0.2-6-15.1.1

  (1,16) (2,20) (3,19) (4,18) (5,17) (6,21) (7,25) (8,24) (9,23) (10,22) (11,26) (12,30) (13,29) (14,28) (15,27)
  (1,23,11,18,6,28) (2,22,12,17,7,27) (3,21,13,16,8,26) (4,25,14,20,9,30) (5,24,15,19,10,29)
  (1,14,7,5,13,6,4,12,10,3,11,9,2,15,8) (16,29,22,20,28,21,19,27,25,18,26,24,17,30,23)