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, 3, 3, 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.

5.20-4.0.2-2-2-10.1.1

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