Properties

Label 7.64-38.0.2-4-16.12
Genus \(7\)
Quotient genus \(0\)
Group \(D_8:C_4\)
Signature \([ 0; 2, 4, 16 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $7$
Quotient genus: $0$
Group name: $D_8:C_4$
Group identifier: $[64,38]$
Signature: $[ 0; 2, 4, 16 ]$
Conjugacy classes for this refined passport: $6, 9, 21$

Jacobian variety group algebra decomposition:$E\times E^{2}\times A_{2}^{2}$
Corresponding character(s): $6, 12, 17$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,5) (2,6) (3,7) (4,8) (9,13) (10,14) (11,15) (12,16) (17,21) (18,22) (19,23) (20,24) (25,29) (26,30) (27,31) (28,32) (33,37) (34,38) (35,39) (36,40) (41,45) (42,46) (43,47) (44,48) (49,53) (50,54) (51,55) (52,56) (57,61) (58,62) (59,63) (60,64)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{16}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

7.64-38.0.2-4-16.12.1

  (1,21) (2,22) (3,24) (4,23) (5,17) (6,18) (7,20) (8,19) (9,31) (10,32) (11,29) (12,30) (13,27) (14,28) (15,25) (16,26) (33,53) (34,54) (35,56) (36,55) (37,49) (38,50) (39,52) (40,51) (41,63) (42,64) (43,61) (44,62) (45,59) (46,60) (47,57) (48,58)
  (1,35,5,39) (2,36,6,40) (3,33,7,37) (4,34,8,38) (9,42,13,46) (10,41,14,45) (11,43,15,47) (12,44,16,48) (17,59,21,63) (18,60,22,64) (19,57,23,61) (20,58,24,62) (25,51,29,55) (26,52,30,56) (27,49,31,53) (28,50,32,54)
  (1,52,16,62,3,49,13,64,2,51,15,61,4,50,14,63) (5,56,12,58,7,53,9,60,6,55,11,57,8,54,10,59) (17,41,32,38,19,43,29,40,18,42,31,37,20,44,30,39) (21,45,28,34,23,47,25,36,22,46,27,33,24,48,26,35)