Properties

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

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Family Information

Genus: 12
Group name: $C_{50}$
Group identifier: [50,2]
Signature: $[ 0; 2, 25, 50 ]$
Conjugacy classes for this refined passport: 2, 11, 50

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.

12.50-2.0.2-25-50.1.1

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