Properties

Label 15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1273
Genus \(15\)
Quotient genus \(0\)
Group \(C_2^3\)
Signature \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $15$
Quotient genus: $0$
Group name: $C_2^3$
Group identifier: $[8,5]$
Signature: $[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$
Conjugacy classes for this refined passport: $3, 5, 7, 8, 8, 8, 8, 8, 8, 8, 8$

Jacobian variety group algebra decomposition:$A_{3}\times A_{4}\times A_{4}\times A_{4}$
Corresponding character(s): $2, 3, 5, 8$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,8) (2,7) (3,6) (4,5)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)(x^{4}+a_{3}x^{2}+1)(x^{4}+a_{4}x^{2}+1)(x^{4}+a_{5}x^{2}+1)(x^{4}+a_{6}x^{2}+1)(x^{4}+a_{7}x^{2}+1)(x^{4}+a_{8}x^{2}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1273.1

  (1,3) (2,4) (5,7) (6,8)
  (1,5) (2,6) (3,7) (4,8)
  (1,7) (2,8) (3,5) (4,6)
  (1,8) (2,7) (3,6) (4,5)
  (1,8) (2,7) (3,6) (4,5)
  (1,8) (2,7) (3,6) (4,5)
  (1,8) (2,7) (3,6) (4,5)
  (1,8) (2,7) (3,6) (4,5)
  (1,8) (2,7) (3,6) (4,5)
  (1,8) (2,7) (3,6) (4,5)
  (1,8) (2,7) (3,6) (4,5)