Properties

Genus \(7\)
Quotient Genus \(0\)
Group \(\PSL(2,8)\)
Signature \([ 0; 2, 3, 7 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 7
Quotient Genus: 0
Group name: $\PSL(2,8)$
Group identifier: [504,156]
Signature: $[ 0; 2, 3, 7 ]$
Conjugacy classes for this refined passport: 2, 3, 4

Jacobian variety group algebra decomposition:$E^{7}$
Corresponding character(s): 2

Other Data

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

7.504-156.0.2-3-7.1.1

  (1,33) (2,263) (3,139) (4,165) (5,493) (6,37) (7,257) (8,153) (9,368) (10,51) (11,380) (12,301) (13,228) (14,160) (15,19) (16,374) (17,252) (18,143) (20,155) (21,364) (22,462) (23,115) (24,55) (25,194) (26,486) (27,278) (28,60) (29,209) (30,94) (31,417) (32,268) (34,68) (35,405) (36,305) (38,488) (39,274) (40,120) (41,295) (42,46) (43,455) (44,135) (45,179) (47,290) (48,472) (49,354) (50,385) (52,320) (53,288) (54,98) (56,110) (57,175) (58,327) (59,214) (61,77) (62,315) (63,476) (64,429) (65,389) (66,265) (67,435) (69,208) (70,419) (71,450) (72,341) (73,105) (74,335) (75,211) (76,237) (78,109) (79,329) (80,225) (81,440) (82,123) (83,452) (84,373) (85,300) (86,232) (87,91) (88,446) (89,324) (90,215) (92,227) (93,436) (95,187) (96,127) (97,266) (99,350) (100,132) (101,281) (102,166) (103,489) (104,340) (106,140) (107,477) (108,377) (111,346) (112,192) (113,367) (114,118) (116,207) (117,251) (119,362) (121,426) (122,457) (124,392) (125,360) (126,170) (128,182) (129,247) (130,399) (131,286) (133,149) (134,387) (136,501) (137,461) (138,337) (141,280) (142,491) (144,413) (145,177) (146,407) (147,283) (148,309) (150,181) (151,401) (152,297) (154,195) (156,445) (157,372) (158,304) (159,163) (161,396) (162,287) (164,299) (167,259) (168,199) (169,338) (171,422) (172,204) (173,353) (174,238) (176,412) (178,212) (180,449) (183,418) (184,264) (185,439) (186,190) (188,279) (189,323) (191,434) (193,498) (196,464) (197,432) (198,242) (200,254) (201,319) (202,471) (203,358) (205,221) (206,459) (210,409) (213,352) (216,485) (217,249) (218,479) (219,355) (220,381) (222,253) (223,473) (224,369) (226,267) (229,444) (230,376) (231,235) (233,468) (234,359) (236,371) (239,331) (240,271) (241,410) (243,494) (244,276) (245,425) (246,310) (248,484) (250,284) (255,490) (256,336) (258,262) (260,351) (261,395) (269,504) (270,314) (272,326) (273,391) (275,430) (277,293) (282,481) (285,424) (289,321) (291,427) (292,453) (294,325) (296,441) (298,339) (302,448) (303,307) (306,431) (308,443) (311,403) (312,343) (313,482) (316,348) (317,497) (318,382) (322,356) (328,408) (330,334) (332,423) (333,467) (342,386) (344,398) (345,463) (347,502) (349,365) (357,496) (361,393) (363,499) (366,397) (370,411) (375,379) (378,503) (383,475) (384,415) (388,420) (390,454) (394,428) (400,480) (402,406) (404,495) (414,458) (416,470) (421,437) (433,465) (438,469) (442,483) (447,451) (456,487) (460,492) (466,500) (474,478)
  (1,198,62) (2,483,238) (3,52,392) (4,110,384) (5,129,79) (6,247,371) (7,437,57) (8,46,72) (9,467,469) (10,261,44) (11,150,391) (12,61,500) (13,488,213) (14,480,457) (15,400,65) (16,203,39) (17,55,324) (18,170,172) (19,459,53) (20,132,202) (21,34,239) (22,290,267) (23,309,322) (24,148,254) (25,86,48) (26,28,378) (27,125,91) (29,249,499) (30,43,338) (31,155,294) (32,147,196) (33,283,317) (35,37,81) (36,233,271) (38,312,436) (40,209,159) (41,282,70) (42,481,191) (45,332,298) (47,402,337) (49,263,114) (50,246,259) (51,310,74) (54,422,361) (56,285,85) (58,380,492) (59,399,376) (60,130,452) (63,359,136) (64,495,287) (66,358,329) (67,101,321) (68,84,133) (69,373,344) (71,352,279) (73,270,134) (75,124,464) (76,182,456) (77,201,151) (78,319,443) (80,118,144) (82,333,116) (83,222,463) (87,472,137) (88,275,111) (89,127,396) (90,242,244) (92,204,274) (93,106,311) (94,362,339) (95,381,394) (96,220,326) (97,158,120) (98,100,450) (99,197,163) (102,115,410) (103,227,366) (104,219,268) (105,355,389) (107,109,153) (108,305,343) (112,281,231) (113,354,142) (117,404,370) (119,474,409) (121,335,186) (122,318,331) (123,382,146) (126,494,433) (128,357,157) (131,471,448) (135,431,208) (138,430,401) (139,173,393) (140,156,205) (141,445,416) (143,424,351) (145,342,206) (149,273,223) (152,190,216) (154,405,188) (160,347,183) (161,199,468) (162,314,316) (164,276,346) (165,178,383) (166,434,411) (167,453,466) (168,292,398) (169,230,192) (171,269,235) (174,187,482) (175,299,438) (176,291,340) (177,427,461) (179,181,225) (180,377,415) (184,353,303) (185,426,214) (189,476,442) (193,407,258) (194,390,403) (195,454,218) (200,429,229) (207,503,280) (210,502,473) (211,245,465) (212,228,277) (215,496,423) (217,414,278) (221,345,295) (224,262,288) (226,477,260) (232,419,255) (234,386,388) (236,348,418) (237,250,455) (240,364,470) (241,302,264) (243,341,307) (248,363,412) (251,253,297) (252,449,487) (256,425,375) (257,498,286) (265,479,330) (266,462,475) (272,501,301) (284,300,349) (289,486,350) (293,417,367) (296,334,360) (304,491,327) (306,458,460) (308,420,490) (313,374,336) (315,413,379) (320,435,484) (323,325,369) (328,497,447) (356,372,421) (365,489,439) (368,406,432) (385,446,408) (387,485,451) (395,397,441) (428,444,493) (440,478,504)
  (1,315,375,245,75,196,283) (2,174,313,256,379,144,114) (3,124,211,433,243,303,173) (4,415,108,312,488,228,178) (5,329,203,374,482,95,428) (6,236,183,502,409,478,81) (7,175,469,333,123,407,498) (8,341,494,170,143,260,107) (9,438,164,111,430,337,406) (10,135,69,398,453,259,310) (11,273,133,373,208,306,492) (12,466,292,199,396,96,272) (13,352,450,132,155,417,277) (14,122,239,68,149,473,347) (15,389,219,340,427,145,459) (16,274,172,126,465,425,336) (17,89,161,233,305,377,449) (18,204,227,489,349,85,424) (19,288,258,146,318,457,400) (20,471,286,193,262,369,294) (21,331,382,82,207,141,470) (22,226,351,285,110,165,475) (23,356,437,257,131,302,410) (24,200,444,394,220,127,324) (25,472,91,360,330,218,390) (26,503,116,467,368,197,350) (27,87,461,291,412,499,217) (28,486,321,281,192,376,130) (29,363,484,67,289,99,159) (30,169,112,235,504,474,362) (31,325,189,483,263,354,367) (32,464,392,320,248,176,104) (33,497,408,88,346,244,198) (34,364,271,468,168,344,84) (35,440,269,422,98,71,188) (36,240,416,156,106,436,343) (37,405,195,479,66,79,247) (38,93,403,454,154,279,213) (39,358,265,334,441,366,92) (40,163,432,402,290,462,97) (41,419,86,194,311,140,221) (42,434,102,241,184,307,72) (43,94,298,423,357,182,237) (44,395,296,125,278,458,431) (45,339,119,210,223,391,181) (46,153,78,308,255,70,481) (47,138,151,319,109,477,267) (48,232,490,388,342,177,137) (49,118,225,150,380,327,142) (50,167,500,77,401,275,446) (51,335,426,439,103,397,261) (52,139,361,171,231,101,435) (53,206,386,359,476,323,224) (54,393,353,264,448,202,100) (55,252,456,128,372,322,148) (56,300,250,76,487,180,384) (57,421,157,496,90,276,299) (58,460,414,249,209,120,304) (59,230,338,455,284,365,185) (60,83,345,205,445,280,378) (61,301,136,234,420,443,201) (62,242,215,332,179,80,413) (63,501,326,381,187,238,442) (64,162,348,371,129,493,229) (65,480,160,418,316,270,105) (73,387,447,317,147,268,355) (74,246,385,328,451,216,186) (113,491,158,266,383,212,293) (115,166,370,495,429,254,309) (117,411,191,282,295,463,253) (121,190,297,222,452,399,214) (134,314,287,404,251,152,485)