Properties

Genus \(7\)
Quotient Genus \(0\)
Group \(C_{30}\)
Signature \([ 0; 2, 15, 30 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 7
Quotient Genus: 0
Group name: $C_{30}$
Group identifier: [30,4]
Signature: $[ 0; 2, 15, 30 ]$
Conjugacy classes for this refined passport: 2, 16, 26

Jacobian variety group algebra decomposition:$E\times A_{2}\times A_{4}$
Corresponding character(s): 4, 8, 10

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{15}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

7.30-4.0.2-15-30.2.1

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