Properties

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

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $D_{10}$
Group identifier: [20,4]
Signature: $[ 0; 2, 2, 2, 2, 10 ]$
Conjugacy classes for this refined passport: 2, 2, 3, 4, 8

Jacobian variety group algebra decomposition:$E\times E\times A_{4}^{2}$
Corresponding character(s): 3, 4, 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:
  $y^2=x(x^{10}+a_{1}x^{5}+1)(x^{10}+a_{2}x^{5}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.20-4.0.2-2-2-2-10.2.1

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