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, 16

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.

10.88-7.0.2-4-22.1.1

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