Properties

Label 7.30-4.0.2-15-30.4
Genus \(7\)
Quotient genus \(0\)
Group \(C_{30}\)
Signature \([ 0; 2, 15, 30 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $7$
Quotient genus: $0$
Group name: $C_{30}$
Group identifier: $[30,4]$
Signature: $[ 0; 2, 15, 30 ]$
Conjugacy classes for this refined passport: $2, 18, 29$

Jacobian variety group algebra decomposition:$E\times A_{2}\times A_{4}$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,16) (2,17) (3,18) (4,19) (5,20) (6,21) (7,22) (8,23) (9,24) (10,25) (11,26) (12,27) (13,28) (14,29) (15,30)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{15}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

7.30-4.0.2-15-30.4.1

  (1,16) (2,17) (3,18) (4,19) (5,20) (6,21) (7,22) (8,23) (9,24) (10,25) (11,26) (12,27) (13,28) (14,29) (15,30)
  (1,8,15,2,9,11,3,10,12,4,6,13,5,7,14) (16,23,30,17,24,26,18,25,27,19,21,28,20,22,29)
  (1,29,7,20,13,21,4,27,10,18,11,24,2,30,8,16,14,22,5,28,6,19,12,25,3,26,9,17,15,23)