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Properties

Label 11.88-4.0.2-4-44.15
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: $4, 7, 26$

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

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.

11.88-4.0.2-4-44.15.1

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