Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(D_{22}\)
Signature \([ 0; 2, 2, 2, 11 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $D_{22}$
Group identifier: [44,3]
Signature: $[ 0; 2, 2, 2, 11 ]$
Conjugacy classes for this refined passport: 2, 3, 4, 5

Jacobian variety group algebra decomposition:$A_{5}^{2}$
Corresponding character(s): 6

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{22}+a_1x^{11}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.44-3.0.2-2-2-11.1.1

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