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, 22, 41

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.

10.42-6.0.2-21-42.4.1

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