Properties

Label 11.12-5.0.2-2-2-2-6-6.2
Genus \(11\)
Quotient genus \(0\)
Group \(C_2\times C_6\)
Signature \([ 0; 2, 2, 2, 2, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $11$
Quotient genus: $0$
Group name: $C_2\times C_6$
Group identifier: $[12,5]$
Signature: $[ 0; 2, 2, 2, 2, 6, 6 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 2, 11, 12$

Jacobian variety group algebra decomposition:$A_{2}\times E\times A_{4}\times A_{4}$
Corresponding character(s): $3, 4, 7, 8$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{24}+a_{1}x^{18}+a_{2}x^{12}+a_{3}x^{6}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

11.12-5.0.2-2-2-2-6-6.2.1

  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,11,3,10,2,12) (4,8,6,7,5,9)
  (1,12,2,10,3,11) (4,9,5,7,6,8)