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Properties

Label 11.88-4.0.2-4-44.13
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: $4, 7, 23$

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.

11.88-4.0.2-4-44.13.1

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