Properties

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

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $D_{22}:C_2$
Group identifier: [88,7]
Signature: $[ 0; 2, 4, 22 ]$
Conjugacy classes for this refined passport: 4, 5, 25

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.

10.88-7.0.2-4-22.10.1

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