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, 26, 39

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.

10.42-6.0.2-21-42.8.1

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