Properties

Genus \(10\)
Small Group \(D_{22}:C_2\)
Signature \([ 0; 2, 4, 22 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Group name: $D_{22}:C_2$
Group identifier: [88,7]
Signature: $[ 0; 2, 4, 22 ]$
Conjugacy classes for this refined passport: 4, 5, 24

Jacobian variety group algebra decomposition:$A_{5}^{2}$
Corresponding character(s): 6

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,12) (2,13) (3,14) (4,15) (5,16) (6,17) (7,18) (8,19) (9,20) (10,21) (11,22) (23,34) (24,35) (25,36) (26,37) (27,38) (28,39) (29,40) (30,41) (31,42) (32,43) (33,44) (45,56) (46,57) (47,58) (48,59) (49,60) (50,61) (51,62) (52,63) (53,64) (54,65) (55,66) (67,78) (68,79) (69,80) (70,81) (71,82) (72,83) (73,84) (74,85) (75,86) (76,87) (77,88)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{22}-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.88-7.0.2-4-22.9.1

  (1,45) (2,55) (3,54) (4,53) (5,52) (6,51) (7,50) (8,49) (9,48) (10,47) (11,46) (12,56) (13,66) (14,65) (15,64) (16,63) (17,62) (18,61) (19,60) (20,59) (21,58) (22,57) (23,78) (24,88) (25,87) (26,86) (27,85) (28,84) (29,83) (30,82) (31,81) (32,80) (33,79) (34,67) (35,77) (36,76) (37,75) (38,74) (39,73) (40,72) (41,71) (42,70) (43,69) (44,68)
  (1,70,12,81) (2,69,13,80) (3,68,14,79) (4,67,15,78) (5,77,16,88) (6,76,17,87) (7,75,18,86) (8,74,19,85) (9,73,20,84) (10,72,21,83) (11,71,22,82) (23,59,34,48) (24,58,35,47) (25,57,36,46) (26,56,37,45) (27,66,38,55) (28,65,39,54) (29,64,40,53) (30,63,41,52) (31,62,42,51) (32,61,43,50) (33,60,44,49)
  (1,31,6,25,11,30,5,24,10,29,4,23,9,28,3,33,8,27,2,32,7,26) (12,42,17,36,22,41,16,35,21,40,15,34,20,39,14,44,19,38,13,43,18,37) (45,75,50,69,55,74,49,68,54,73,48,67,53,72,47,77,52,71,46,76,51,70) (56,86,61,80,66,85,60,79,65,84,59,78,64,83,58,88,63,82,57,87,62,81)