Properties

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

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_{42}$
Group identifier: [42,6]
Signature: $[ 0; 2, 21, 42 ]$
Conjugacy classes for this refined passport: 2, 19, 42

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.

10.42-6.0.2-21-42.1.1

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