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, 21, 35

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.

10.42-6.0.2-21-42.3.1

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