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, 6, 25

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.

8.34-2.0.2-17-34.4.1

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