Properties

Label 14.28-3.0.2-2-2-2-14.3
Genus \(14\)
Quotient genus \(0\)
Group \(D_{14}\)
Signature \([ 0; 2, 2, 2, 2, 14 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $14$
Quotient genus: $0$
Group name: $D_{14}$
Group identifier: $[28,3]$
Signature: $[ 0; 2, 2, 2, 2, 14 ]$
Conjugacy classes for this refined passport: $2, 2, 3, 4, 10$

Jacobian variety group algebra decomposition:$E\times E\times A_{6}^{2}$
Corresponding character(s): $2, 4, 7$

Other Data

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

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.28-3.0.2-2-2-2-14.3.1

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