Properties

Genus \(7\)
Quotient Genus \(0\)
Group \(C_2^2.D_8\)
Signature \([ 0; 2, 4, 16 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 7
Quotient Genus: 0
Group name: $C_2^2.D_8$
Group identifier: [64,38]
Signature: $[ 0; 2, 4, 16 ]$
Conjugacy classes for this refined passport: 5, 9, 16

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.

7.64-38.0.2-4-16.1.1

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