Properties

Genus \(10\)
Small Group \(C_{42}\)
Signature \([ 0; 2, 21, 42 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Group name: $C_{42}$
Group identifier: [42,6]
Signature: $[ 0; 2, 21, 42 ]$
Conjugacy classes for this refined passport: 2, 27, 32

Jacobian variety group algebra decomposition:$E\times A_{3}\times A_{6}$
Corresponding character(s): 4, 8, 10

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,22) (2,23) (3,24) (4,25) (5,26) (6,27) (7,28) (8,29) (9,30) (10,31) (11,32) (12,33) (13,34) (14,35) (15,36) (16,37) (17,38) (18,39) (19,40) (20,41) (21,42)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{21}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.42-6.0.2-21-42.9.1

  (1,22) (2,23) (3,24) (4,25) (5,26) (6,27) (7,28) (8,29) (9,30) (10,31) (11,32) (12,33) (13,34) (14,35) (15,36) (16,37) (17,38) (18,39) (19,40) (20,41) (21,42)
  (1,10,19,7,9,18,6,8,17,5,14,16,4,13,15,3,12,21,2,11,20) (22,31,40,28,30,39,27,29,38,26,35,37,25,34,36,24,33,42,23,32,41)
  (1,41,11,23,21,33,3,36,13,25,16,35,5,38,8,27,18,30,7,40,10,22,20,32,2,42,12,24,15,34,4,37,14,26,17,29,6,39,9,28,19,31)