Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(C_2\times He_3\)
Signature \([ 0; 3, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_2\times He_3$
Group identifier: [54,10]
Signature: $[ 0; 3, 6, 6 ]$
Conjugacy classes for this refined passport: 5, 17, 20

The full automorphism group for this family is $C_2\times He_3:C_2$ with signature $[ 0; 2, 6, 6 ]$.

Jacobian variety group algebra decomposition:$E\times E\times E\times E\times A_{2}^{3}$
Corresponding character(s): 4, 5, 6, 10, 19

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.54-10.0.3-6-6.1.1

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