Properties

Label 15.120-27.0.2-4-60.13
Genus \(15\)
Quotient genus \(0\)
Group \(C_4\times D_{15}\)
Signature \([ 0; 2, 4, 60 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more

Family Information

Genus: $15$
Quotient genus: $0$
Group name: $C_4\times D_{15}$
Group identifier: $[120,27]$
Signature: $[ 0; 2, 4, 60 ]$
Conjugacy classes for this refined passport: $4, 9, 30$

Jacobian variety group algebra decomposition:$E\times E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s): $6, 11, 25, 29$

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:
  $y^2=x(x^{30}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.120-27.0.2-4-60.13.1

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