Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(C_6\times D_5\)
Signature \([ 0; 2, 6, 30 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_6\times D_5$
Group identifier: [60,10]
Signature: $[ 0; 2, 6, 30 ]$
Conjugacy classes for this refined passport: 3, 13, 23

Jacobian variety group algebra decomposition:$E\times E\times A_{2}^{2}\times A_{2}^{2}$
Corresponding character(s): 5, 7, 17, 19

Other Data

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.60-10.0.2-6-30.1.1

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