Properties

Genus \(14\)
Quotient Genus \(0\)
Group \(D_{30}:C_2\)
Signature \([ 0; 2, 4, 30 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 14
Quotient Genus: 0
Group name: $D_{30}:C_2$
Group identifier: [120,30]
Signature: $[ 0; 2, 4, 30 ]$
Conjugacy classes for this refined passport: 4, 6, 27

Jacobian variety group algebra decomposition:$E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s): 8, 10, 18

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{30}-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

14.120-30.0.2-4-30.2.1

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