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Properties

Label 11.88-4.0.2-4-44.17
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: $4, 8, 22$

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.

11.88-4.0.2-4-44.17.1

  (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)
  (1,82,12,71) (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)
  (1,41,15,33,7,36,21,28,2,42,16,23,8,37,22,29,3,43,17,24,9,38,12,30,4,44,18,25,10,39,13,31,5,34,19,26,11,40,14,32,6,35,20,27) (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)