Properties

Genus \(8\)
Quotient Genus \(0\)
Group \(C_{34}\)
Signature \([ 0; 2, 17, 34 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Quotient Genus: 0
Group name: $C_{34}$
Group identifier: [34,2]
Signature: $[ 0; 2, 17, 34 ]$
Conjugacy classes for this refined passport: 2, 17, 27

Jacobian variety group algebra decomposition:$A_{8}$
Corresponding character(s): 4

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,18) (2,19) (3,20) (4,21) (5,22) (6,23) (7,24) (8,25) (9,26) (10,27) (11,28) (12,29) (13,30) (14,31) (15,32) (16,33) (17,34)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{17}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.34-2.0.2-17-34.15.1

  (1,18) (2,19) (3,20) (4,21) (5,22) (6,23) (7,24) (8,25) (9,26) (10,27) (11,28) (12,29) (13,30) (14,31) (15,32) (16,33) (17,34)
  (1,16,14,12,10,8,6,4,2,17,15,13,11,9,7,5,3) (18,33,31,29,27,25,23,21,19,34,32,30,28,26,24,22,20)
  (1,20,5,24,9,28,13,32,17,19,4,23,8,27,12,31,16,18,3,22,7,26,11,30,15,34,2,21,6,25,10,29,14,33)