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, 21

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.

10.80-6.0.2-4-40.6.1

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