Properties

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

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_8:D_5$
Group identifier: [80,6]
Signature: $[ 0; 2, 4, 40 ]$
Conjugacy classes for this refined passport: 3, 5, 23

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.

10.80-6.0.2-4-40.8.1

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