Properties

Label 10.72-23.0.2-6-12.1
Genus \(10\)
Quotient genus \(0\)
Group \(C_3:D_{12}\)
Signature \([ 0; 2, 6, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $10$
Quotient genus: $0$
Group name: $C_3:D_{12}$
Group identifier: $[72,23]$
Signature: $[ 0; 2, 6, 12 ]$
Conjugacy classes for this refined passport: $4, 12, 14$

Jacobian variety group algebra decomposition:$E^{2}\times E^{4}\times E^{4}$
Corresponding character(s): $10, 14, 15$

Other Data

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

10.72-23.0.2-6-12.1.1

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