Properties

Label 10.81-9.0.3-3-9.18
Genus \(10\)
Quotient genus \(0\)
Group \(\He_3:C_3\)
Signature \([ 0; 3, 3, 9 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $10$
Quotient genus: $0$
Group name: $\He_3:C_3$
Group identifier: $[81,9]$
Signature: $[ 0; 3, 3, 9 ]$
Conjugacy classes for this refined passport: $9, 10, 17$

The full automorphism group for this family is $\He_3.C_6$ with signature $[ 0; 2, 3, 18 ]$.

Jacobian variety group algebra decomposition:$E\times A_{3}^{3}$
Corresponding character(s): $2, 12$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

10.81-9.0.3-3-9.18.1

  (1,76,37) (2,77,38) (3,78,39) (4,81,41) (5,79,42) (6,80,40) (7,74,45) (8,75,43) (9,73,44) (10,55,49) (11,56,50) (12,57,51) (13,60,53) (14,58,54) (15,59,52) (16,62,48) (17,63,46) (18,61,47) (19,71,36) (20,72,34) (21,70,35) (22,64,28) (23,65,29) (24,66,30) (25,69,32) (26,67,33) (27,68,31)
  (1,46,72) (2,47,70) (3,48,71) (4,50,65) (5,51,66) (6,49,64) (7,54,67) (8,52,68) (9,53,69) (10,33,76) (11,31,77) (12,32,78) (13,34,81) (14,35,79) (15,36,80) (16,29,74) (17,30,75) (18,28,73) (19,45,55) (20,43,56) (21,44,57) (22,37,60) (23,38,58) (24,39,59) (25,41,62) (26,42,63) (27,40,61)
  (1,20,11,2,21,12,3,19,10) (4,23,14,5,24,15,6,22,13) (7,26,17,8,27,18,9,25,16) (28,47,38,29,48,39,30,46,37) (31,50,41,32,51,42,33,49,40) (34,53,44,35,54,45,36,52,43) (55,74,65,56,75,66,57,73,64) (58,77,68,59,78,69,60,76,67) (61,80,71,62,81,72,63,79,70)