Properties

Label 7.56-4.0.2-4-28.3
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: $3, 7, 20$

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.

7.56-4.0.2-4-28.3.1

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