Properties

Label 7.56-4.0.2-4-28.12
Genus \(7\)
Quotient genus \(0\)
Group \(C_4\times D_7\)
Signature \([ 0; 2, 4, 28 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $7$
Quotient genus: $0$
Group name: $C_4\times D_7$
Group identifier: $[56,4]$
Signature: $[ 0; 2, 4, 28 ]$
Conjugacy classes for this refined passport: $4, 8, 20$

Jacobian variety group algebra decomposition:$E\times A_{3}^{2}$
Corresponding character(s): $5, 15$

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) (29,36) (30,37) (31,38) (32,39) (33,40) (34,41) (35,42) (43,50) (44,51) (45,52) (46,53) (47,54) (48,55) (49,56)
Cyclic trigonal curve(s):no

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

7.56-4.0.2-4-28.12.1

  (1,36) (2,42) (3,41) (4,40) (5,39) (6,38) (7,37) (8,29) (9,35) (10,34) (11,33) (12,32) (13,31) (14,30) (15,50) (16,56) (17,55) (18,54) (19,53) (20,52) (21,51) (22,43) (23,49) (24,48) (25,47) (26,46) (27,45) (28,44)
  (1,56,8,49) (2,55,9,48) (3,54,10,47) (4,53,11,46) (5,52,12,45) (6,51,13,44) (7,50,14,43) (15,35,22,42) (16,34,23,41) (17,33,24,40) (18,32,25,39) (19,31,26,38) (20,30,27,37) (21,29,28,36)
  (1,23,10,18,5,27,14,15,2,24,11,19,6,28,8,16,3,25,12,20,7,22,9,17,4,26,13,21) (29,51,38,46,33,55,42,43,30,52,39,47,34,56,36,44,31,53,40,48,35,50,37,45,32,54,41,49)