Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(SD_{32}\)
Signature \([ 0; 2, 2, 4, 16 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $SD_{32}$
Group identifier: [32,19]
Signature: $[ 0; 2, 2, 4, 16 ]$
Conjugacy classes for this refined passport: 2, 3, 5, 9

Jacobian variety group algebra decomposition:$A_{6}^{2}$
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:
  $y^2=x(x^{8}-1)(x^{16}+a_{1}x^{8}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.32-19.0.2-2-4-16.2.1

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