Properties

Label 6.56-7.0.2-4-14.6
Genus \(6\)
Quotient genus \(0\)
Group \(D_{14}:C_2\)
Signature \([ 0; 2, 4, 14 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more

Family Information

Genus: $6$
Quotient genus: $0$
Group name: $D_{14}:C_2$
Group identifier: $[56,7]$
Signature: $[ 0; 2, 4, 14 ]$
Conjugacy classes for this refined passport: $4, 5, 17$

Jacobian variety group algebra decomposition:$A_{3}^{2}$
Corresponding character(s): $6$

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:
  $y^2=x^{14}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.56-7.0.2-4-14.6.1

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