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: 4, 8, 14

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.

5.40-5.0.2-4-20.7.1

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