Properties

Genus \(8\)
Small Group \(SD_{64}\)
Signature \([ 0; 2, 4, 32 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Group name: $SD_{64}$
Group identifier: [64,53]
Signature: $[ 0; 2, 4, 32 ]$
Conjugacy classes for this refined passport: 3, 5, 13

Jacobian variety group algebra decomposition:$A_{4}^{2}$
Corresponding character(s): 12

Other Data

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

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.64-53.0.2-4-32.2.1

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