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Properties

Label 11.88-4.0.2-4-44.2
Genus \(11\)
Quotient genus \(0\)
Group \(C_4\times D_{11}\)
Signature \([ 0; 2, 4, 44 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $11$
Quotient genus: $0$
Group name: $C_4\times D_{11}$
Group identifier: $[88,4]$
Signature: $[ 0; 2, 4, 44 ]$
Conjugacy classes for this refined passport: $3, 7, 22$

Jacobian variety group algebra decomposition:$E\times A_{5}^{2}$
Corresponding character(s): $6, 19$

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:
  $y^2=x(x^{22}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

11.88-4.0.2-4-44.2.1

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