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, 10

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.

5.120-35.0.2-3-10.2.1

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