Properties

Genus \(5\)
Small Group \(C_4\times D_5\)
Signature \([ 0; 2, 4, 20 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more about

Family Information

Genus: 5
Group name: $C_4\times D_5$
Group identifier: [40,5]
Signature: $[ 0; 2, 4, 20 ]$
Conjugacy classes for this refined passport: 3, 8, 13

Jacobian variety group algebra decomposition:$E\times A_{2}^{2}$
Corresponding character(s): 6, 13

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{10}-1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.40-5.0.2-4-20.3.1

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