Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(C_{50}\)
Signature \([ 0; 2, 25, 50 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $C_{50}$
Group identifier: [50,2]
Signature: $[ 0; 2, 25, 50 ]$
Conjugacy classes for this refined passport: 2, 26, 43

Jacobian variety group algebra decomposition:$A_{10}\times A_{2}$
Corresponding character(s): 4, 12

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,26) (2,27) (3,28) (4,29) (5,30) (6,31) (7,32) (8,33) (9,34) (10,35) (11,36) (12,37) (13,38) (14,39) (15,40) (16,41) (17,42) (18,43) (19,44) (20,45) (21,46) (22,47) (23,48) (24,49) (25,50)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{25}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.50-2.0.2-25-50.16.1

  (1,26) (2,27) (3,28) (4,29) (5,30) (6,31) (7,32) (8,33) (9,34) (10,35) (11,36) (12,37) (13,38) (14,39) (15,40) (16,41) (17,42) (18,43) (19,44) (20,45) (21,46) (22,47) (23,48) (24,49) (25,50)
  (1,24,18,12,6,5,23,17,11,10,4,22,16,15,9,3,21,20,14,8,2,25,19,13,7) (26,49,43,37,31,30,48,42,36,35,29,47,41,40,34,28,46,45,39,33,27,50,44,38,32)
  (1,32,13,44,25,27,8,39,20,46,3,34,15,41,22,29,10,36,17,48,5,31,12,43,24,26,7,38,19,50,2,33,14,45,21,28,9,40,16,47,4,35,11,42,23,30,6,37,18,49)