Properties

Label 6.48-29.0.2-6-8.2
Genus \(6\)
Quotient genus \(0\)
Group \(\GL(2,3)\)
Signature \([ 0; 2, 6, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $6$
Quotient genus: $0$
Group name: $\GL(2,3)$
Group identifier: $[48,29]$
Signature: $[ 0; 2, 6, 8 ]$
Conjugacy classes for this refined passport: $3, 6, 8$

Jacobian variety group algebra decomposition:$E^{2}\times E^{4}$
Corresponding character(s): $4, 8$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) (33,34) (35,36) (37,38) (39,40) (41,42) (43,44) (45,46) (47,48)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^4-1)(x^8+14x^4+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.48-29.0.2-6-8.2.1

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