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, 22

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.

10.80-6.0.2-4-40.7.1

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