Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(C_{14}\)
Signature \([ 0; 2, 2, 2, 7, 14 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_{14}$
Group identifier: [14,2]
Signature: $[ 0; 2, 2, 2, 7, 14 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 5, 13

Jacobian variety group algebra decomposition:$E\times A_{9}$
Corresponding character(s): 2, 4

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{21}+a_{1}x^{14}+a_{2}x^{7}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.14-2.0.2-2-2-7-14.3.1

  (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14)
  (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14)
  (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14)
  (1,4,7,3,6,2,5) (8,11,14,10,13,9,12)
  (1,12,2,13,3,14,4,8,5,9,6,10,7,11)