Properties

Label 9.72-5.0.2-4-36.2
Genus \(9\)
Quotient genus \(0\)
Group \(C_4\times D_9\)
Signature \([ 0; 2, 4, 36 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $9$
Quotient genus: $0$
Group name: $C_4\times D_9$
Group identifier: $[72,5]$
Signature: $[ 0; 2, 4, 36 ]$
Conjugacy classes for this refined passport: $3, 8, 23$

Jacobian variety group algebra decomposition:$E\times E^{2}\times A_{3}^{2}$
Corresponding character(s): $5, 11, 19$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18) (19,28) (20,29) (21,30) (22,31) (23,32) (24,33) (25,34) (26,35) (27,36) (37,46) (38,47) (39,48) (40,49) (41,50) (42,51) (43,52) (44,53) (45,54) (55,64) (56,65) (57,66) (58,67) (59,68) (60,69) (61,70) (62,71) (63,72)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{18}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.72-5.0.2-4-36.2.1

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