Properties

Genus \(10\)
Small Group \(C_8:D_5\)
Signature \([ 0; 2, 4, 40 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Group name: $C_8:D_5$
Group identifier: [80,6]
Signature: $[ 0; 2, 4, 40 ]$
Conjugacy classes for this refined passport: 3, 5, 19

Jacobian variety group algebra decomposition:$E^{2}\times A_{4}^{2}$
Corresponding character(s): 10, 16

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) (21,26) (22,27) (23,28) (24,29) (25,30) (31,36) (32,37) (33,38) (34,39) (35,40) (41,46) (42,47) (43,48) (44,49) (45,50) (51,56) (52,57) (53,58) (54,59) (55,60) (61,66) (62,67) (63,68) (64,69) (65,70) (71,76) (72,77) (73,78) (74,79) (75,80)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{20}-1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.80-6.0.2-4-40.4.1

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