Properties

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

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Family Information

Genus: 8
Group name: $C_{34}$
Group identifier: [34,2]
Signature: $[ 0; 2, 17, 34 ]$
Conjugacy classes for this refined passport: 2, 4, 26

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.

8.34-2.0.2-17-34.2.1

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