Properties

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

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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, 7, 15

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.

5.40-5.0.2-4-20.2.1

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