Properties

Label 15.128-147.0.2-4-32.15
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: $5, 10, 35$

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.

15.128-147.0.2-4-32.15.1

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