Properties

Genus \(5\)
Quotient Genus \(0\)
Group \(D_{10}\)
Signature \([ 0; 2, 2, 2, 10 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Quotient Genus: 0
Group name: $D_{10}$
Group identifier: [20,4]
Signature: $[ 0; 2, 2, 2, 10 ]$
Conjugacy classes for this refined passport: 2, 4, 4, 7

Jacobian variety group algebra decomposition:$E\times A_{2}^{2}$
Corresponding character(s): 3, 5

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)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{10}+a_{1}x^{5}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.20-4.0.2-2-2-10.3.1

  (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20)
  (1,16) (2,20) (3,19) (4,18) (5,17) (6,11) (7,15) (8,14) (9,13) (10,12)
  (1,20) (2,19) (3,18) (4,17) (5,16) (6,15) (7,14) (8,13) (9,12) (10,11)
  (1,7,3,9,5,6,2,8,4,10) (11,17,13,19,15,16,12,18,14,20)