Properties

Label 12.50-2.0.2-25-50.11
Genus \(12\)
Quotient genus \(0\)
Group \(C_{50}\)
Signature \([ 0; 2, 25, 50 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more

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: $2, 21, 45$

Jacobian variety group algebra decomposition:$A_{10}\times A_{2}$

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.

12.50-2.0.2-25-50.11.1

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