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, 15, 30

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.

7.30-4.0.2-15-30.1.1

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