Properties

Genus \(3\)
Quotient Genus \(0\)
Group \(\PSL(2,7)\)
Signature \([ 0; 2, 3, 7 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 3
Quotient Genus: 0
Group name: $\PSL(2,7)$
Group identifier: [168,42]
Signature: $[ 0; 2, 3, 7 ]$
Conjugacy classes for this refined passport: 2, 3, 6

Jacobian variety group algebra decomposition:$E^{3}$
Corresponding character(s): 2

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $x^3y+y^3z+z^3x=0$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

3.168-42.0.2-3-7.2.1

  (1,5) (2,9) (3,45) (4,88) (6,77) (7,104) (8,12) (10,17) (11,32) (13,154) (14,125) (15,19) (16,23) (18,39) (20,91) (21,160) (22,26) (24,66) (25,151) (27,84) (28,139) (29,33) (30,114) (31,38) (34,147) (35,48) (36,40) (37,163) (41,98) (42,69) (43,47) (44,51) (46,130) (49,146) (50,54) (52,59) (53,74) (55,112) (56,167) (57,61) (58,65) (60,81) (62,133) (63,118) (64,68) (67,109) (70,97) (71,75) (72,156) (73,80) (76,105) (78,82) (79,121) (83,140) (85,89) (86,93) (87,129) (90,161) (92,96) (94,101) (95,116) (99,103) (100,107) (102,123) (106,110) (108,150) (111,168) (113,117) (115,122) (119,132) (120,124) (126,153) (127,131) (128,135) (134,138) (136,143) (137,158) (141,145) (142,149) (144,165) (148,152) (155,159) (157,164) (162,166)
  (1,108,81) (2,140,96) (3,116,148) (4,141,115) (5,30,28) (6,83,146) (7,26,37) (8,80,109) (9,168,117) (10,95,71) (11,155,94) (12,86,56) (13,111,160) (14,54,128) (15,73,130) (16,119,166) (17,144,78) (18,120,143) (19,149,63) (20,132,125) (21,61,107) (22,129,74) (23,105,145) (24,165,85) (25,92,164) (27,76,97) (29,52,137) (31,88,57) (32,64,87) (33,93,84) (34,139,69) (35,82,100) (36,59,102) (38,151,50) (39,43,150) (40,142,77) (41,104,48) (42,75,135) (44,98,138) (45,158,106) (46,99,157) (47,72,70) (49,68,79) (51,126,159) (53,113,136) (55,153,118) (58,161,124) (60,162,101) (62,90,167) (65,147,103) (66,123,127) (67,134,122) (89,114,112) (91,110,121) (131,156,154) (133,152,163)
  (1,60,94,159,153,112,30) (2,92,151,31,61,160,168) (3,152,62,56,93,29,158) (4,122,138,41,35,107,57) (5,139,147,58,120,39,108) (6,49,121,106,137,59,40) (7,163,148,95,17,82,48) (8,67,115,145,76,84,86) (9,113,74,87,68,146,140) (10,75,69,28,114,85,144) (11,101,166,132,91,79,64) (12,167,161,65,99,130,80) (13,21,100,78,165,66,131) (14,135,71,116,45,110,20) (15,46,164,96,83,77,149) (16,162,81,150,47,97,105) (18,136,117,111,154,72,43) (19,118,126,44,134,109,73) (22,53,143,124,90,133,37) (23,141,88,38,54,125,119) (24,89,55,63,142,36,123) (25,157,103,34,42,128,50) (26,104,98,51,155,32,129) (27,70,156,127,102,52,33)