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, 20

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.

10.80-6.0.2-4-40.5.1

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