Properties

Label 12.32-19.0.2-2-4-16.4
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: $2, 3, 5, 11$

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.

12.32-19.0.2-2-4-16.4.1

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