Properties

Label 11.88-4.0.2-4-44.7
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: $3, 8, 21$

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.

11.88-4.0.2-4-44.7.1

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