Properties

Genus \(8\)
Quotient Genus \(0\)
Group \(D_{16}\)
Signature \([ 0; 2, 2, 2, 16 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Quotient Genus: 0
Group name: $D_{16}$
Group identifier: [32,18]
Signature: $[ 0; 2, 2, 2, 16 ]$
Conjugacy classes for this refined passport: 2, 3, 4, 9

Jacobian variety group algebra decomposition:$A_{4}^{2}$
Corresponding character(s): 8

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{16}+a_{1}x^{8}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.32-18.0.2-2-2-16.2.1

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