Properties

Label 10.60-10.0.2-6-30.7
Genus \(10\)
Quotient genus \(0\)
Group \(C_3\times D_{10}\)
Signature \([ 0; 2, 6, 30 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $10$
Quotient genus: $0$
Group name: $C_3\times D_{10}$
Group identifier: $[60,10]$
Signature: $[ 0; 2, 6, 30 ]$
Conjugacy classes for this refined passport: $4, 12, 21$

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.

10.60-10.0.2-6-30.7.1

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