Properties

Genus \(5\)
Quotient Genus \(0\)
Group \(C_2\times A_5\)
Signature \([ 0; 2, 3, 10 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Quotient Genus: 0
Group name: $C_2\times A_5$
Group identifier: [120,35]
Signature: $[ 0; 2, 3, 10 ]$
Conjugacy classes for this refined passport: 3, 5, 9

Jacobian variety group algebra decomposition:$E^{5}$
Corresponding character(s): 10

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,61) (2,62) (3,63) (4,64) (5,65) (6,66) (7,67) (8,68) (9,69) (10,70) (11,71) (12,72) (13,73) (14,74) (15,75) (16,76) (17,77) (18,78) (19,79) (20,80) (21,81) (22,82) (23,83) (24,84) (25,85) (26,86) (27,87) (28,88) (29,89) (30,90) (31,91) (32,92) (33,93) (34,94) (35,95) (36,96) (37,97) (38,98) (39,99) (40,100) (41,101) (42,102) (43,103) (44,104) (45,105) (46,106) (47,107) (48,108) (49,109) (50,110) (51,111) (52,112) (53,113) (54,114) (55,115) (56,116) (57,117) (58,118) (59,119) (60,120)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{10}+11x^5-1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.120-35.0.2-3-10.1.1

  (1,6) (2,5) (3,14) (4,38) (7,10) (8,29) (9,108) (11,16) (12,15) (13,99) (17,20) (18,104) (19,53) (21,26) (22,25) (23,34) (24,58) (27,30) (28,49) (31,36) (32,35) (33,119) (37,40) (39,73) (41,46) (42,45) (43,54) (44,78) (47,50) (48,69) (51,56) (52,55) (57,60) (59,93) (61,66) (62,65) (63,74) (64,98) (67,70) (68,89) (71,76) (72,75) (77,80) (79,113) (81,86) (82,85) (83,94) (84,118) (87,90) (88,109) (91,96) (92,95) (97,100) (101,106) (102,105) (103,114) (107,110) (111,116) (112,115) (117,120)
  (1,107,69) (2,74,16) (3,98,73) (4,66,97) (5,20,110) (6,37,64) (7,89,21) (8,48,88) (9,61,47) (10,25,40) (11,52,79) (12,39,91) (13,63,38) (14,76,62) (15,95,55) (17,44,106) (18,113,43) (19,71,112) (22,94,36) (23,118,93) (24,86,117) (26,57,84) (27,109,41) (28,68,108) (29,81,67) (30,45,60) (31,72,99) (32,59,111) (33,83,58) (34,96,82) (35,115,75) (42,114,56) (46,77,104) (49,101,87) (50,65,80) (51,92,119) (53,103,78) (54,116,102) (70,85,100) (90,105,120)
  (1,48,29,70,97,61,108,89,10,37) (2,11,113,104,80,62,71,53,44,20) (3,39,15,52,16,63,99,75,112,76) (4,100,82,91,73,64,40,22,31,13) (5,107,6,98,14,65,47,66,38,74) (7,26,118,34,85,67,86,58,94,25) (8,109,30,57,21,68,49,90,117,81) (9,50,77,41,88,69,110,17,101,28) (12,96,23,59,35,72,36,83,119,95) (18,54,105,87,106,78,114,45,27,46) (19,115,32,116,43,79,55,92,56,103) (24,120,102,111,93,84,60,42,51,33)