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, 13, 49

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.

12.50-2.0.2-25-50.3.1

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