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, 15, 38

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.

12.50-2.0.2-25-50.5.1

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