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Properties

Label 11.88-4.0.2-4-44.10
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: $3, 8, 26$

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.

11.88-4.0.2-4-44.10.1

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