Properties

Label 15.128-147.0.2-4-32.16
Genus \(15\)
Quotient genus \(0\)
Group \(D_{16}:C_4\)
Signature \([ 0; 2, 4, 32 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $15$
Quotient genus: $0$
Group name: $D_{16}:C_4$
Group identifier: $[128,147]$
Signature: $[ 0; 2, 4, 32 ]$
Conjugacy classes for this refined passport: $5, 10, 37$

Jacobian variety group algebra decomposition:$E\times E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s): $6, 13, 16, 23$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,9) (2,10) (3,11) (4,12) (5,13) (6,14) (7,15) (8,16) (17,25) (18,26) (19,27) (20,28) (21,29) (22,30) (23,31) (24,32) (33,41) (34,42) (35,43) (36,44) (37,45) (38,46) (39,47) (40,48) (49,57) (50,58) (51,59) (52,60) (53,61) (54,62) (55,63) (56,64) (65,73) (66,74) (67,75) (68,76) (69,77) (70,78) (71,79) (72,80) (81,89) (82,90) (83,91) (84,92) (85,93) (86,94) (87,95) (88,96) (97,105) (98,106) (99,107) (100,108) (101,109) (102,110) (103,111) (104,112) (113,121) (114,122) (115,123) (116,124) (117,125) (118,126) (119,127) (120,128)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{32}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.128-147.0.2-4-32.16.1

  (1,33) (2,34) (3,36) (4,35) (5,39) (6,40) (7,37) (8,38) (9,41) (10,42) (11,44) (12,43) (13,47) (14,48) (15,45) (16,46) (17,53) (18,54) (19,56) (20,55) (21,49) (22,50) (23,52) (24,51) (25,61) (26,62) (27,64) (28,63) (29,57) (30,58) (31,60) (32,59) (65,97) (66,98) (67,100) (68,99) (69,103) (70,104) (71,101) (72,102) (73,105) (74,106) (75,108) (76,107) (77,111) (78,112) (79,109) (80,110) (81,117) (82,118) (83,120) (84,119) (85,113) (86,114) (87,116) (88,115) (89,125) (90,126) (91,128) (92,127) (93,121) (94,122) (95,124) (96,123)
  (1,77,9,69) (2,78,10,70) (3,80,11,72) (4,79,12,71) (5,73,13,65) (6,74,14,66) (7,76,15,68) (8,75,16,67) (17,92,25,84) (18,91,26,83) (19,90,27,82) (20,89,28,81) (21,93,29,85) (22,94,30,86) (23,96,31,88) (24,95,32,87) (33,125,41,117) (34,126,42,118) (35,128,43,120) (36,127,44,119) (37,121,45,113) (38,122,46,114) (39,124,47,116) (40,123,48,115) (49,109,57,101) (50,110,58,102) (51,112,59,104) (52,111,60,103) (53,105,61,97) (54,106,62,98) (55,108,63,100) (56,107,64,99)
  (1,103,31,123,6,98,26,128,4,101,29,121,7,99,27,126,2,104,32,124,5,97,25,127,3,102,30,122,8,100,28,125) (9,111,23,115,14,106,18,120,12,109,21,113,15,107,19,118,10,112,24,116,13,105,17,119,11,110,22,114,16,108,20,117) (33,81,63,75,38,86,58,80,36,84,61,73,39,87,59,78,34,82,64,76,37,85,57,79,35,83,62,74,40,88,60,77) (41,89,55,67,46,94,50,72,44,92,53,65,47,95,51,70,42,90,56,68,45,93,49,71,43,91,54,66,48,96,52,69)