{"label":"415.2.a.a","letter":"a","dim":1,"charpoly":["-10","1"],"traces":["1","1","3","-1","1","3","1","-3","6","1","3","-3","-6","1","3","-1","-7","6","2","-1","3","3","4","-9","1","-6","9","-1","-7","3","5","5","9","-7","1","-6","-7","2","-18","-3","6","3","4","-3","6","4","-4","-3","-6","1","-21","6","-10","9","3","-3","6","-7","-3","-3","5","5","6","7","-6","9","2","7","12","1","14","-18","-4","-7","3","-2","3","-18","-14","-1","9","6","-1","-3","-7","4","-21","-9","12","6","-6","-4","15","-4","2","15","8","-6","18","-1","-10","-21","12","18","3","-10","-2","-9","7","3","-21","-1","11","6","4","7","-36","-3","-7","-9","-2","5","18","-5","1","6","1","-3","12","-6","4","-9","2","2","9","21","-10","12","10","-1","-12","14","-18","-6","-7","-4","-18","7","-12","3","1","-6","-42","3","5","18","-18","-14","-30","5","4","9","-2","-6","9","-1","25","-9","23","-7","12","-4","9","-21","1","-3","-9","12","18","-6","-22","-6","15","-12","-7","15","-21","4","9","2","21","21","-14","8","-18","6","23","18","24","-3","6","-10","-7","21","6","12","24","6","6","3","-4","10","42","-2","4","-27","5","7","-12","-3","42","-21","-16","5","6","11","20","-6","22","4","9","21","18","-36","-4","3","-42","-7","-24","-3","-1","-2","0","-5","-6","18","-12","-15","-3","1","8","-6","12","1","-21","-17","22","12","-7","6","-42","4","2","-27","-10","2","36","-2","6","9","-8","7","-18","-10","3","-12","-30","10","30","-3","8","-12","-14","-14","6","-18","6","30","32","-7","24","4","-22","-18","-3","21","27","-12","-24","-3","4","1","-30","-2","5","-42","12","-3","36","5","-20","54","-1","-18","6","14","-1","-30","-21","7","-6","4","-14","-9","-6","-2","21","-18","-4","9","-18","1","-42","25","2","-3","-26","23","33","7","15","12","-13","-12","12","9","30","21","-9","1","-54","15","19","-9","14","-12","-21","18","-15","-18","-15","-22","-6","6","-4","15","-22","-4","36","-7","-10","-15","-7","-21","3","12","42","9","-24","-2","3","21","-9","-9","3","-14","24","-8","12","-18","-28","18","12","23","-14","-18","10","24","6","-1","-10","6","-30","10","9","-7","-21","63","3","6","-30","-12","-3","24","-1","-30","30","6","-5","-3","30","-4","-24","30","-7","42","5","2","-54","4","-27","-9","-28","5","-21","-7","8","-12","8","-9","-36","42","9","21","12","-16","-36","7","-26","6","18","-11","3","20","-6","-18","-6","22","-63","-4","4","9","7","7","15","18","-40","36","2","-4","-54","9","12","-42","2","7","-60","-24","21","15","42","-1","12","2","8","0","-28","-15","-6","-6","10","-18","49","-12","18","-5","14","-3","31","-1","75","8","0","-18","-10","12","69","-1","-1","-21","-4","-11","18","22","12","-12","-12","-7","27","18","18","-42","17","-4","3","2","-35","-9","-7","-10","-18","-2","-36","36","-2","-6","54","6","-18","-9","-26","-8","-66","-35","7","-18","-15","10","30","3","-14","-36","-14","-30","-21","-10","-42","30","-24","-1","-63","8","-15","12","11","-14","9","-42","-6","6","24","18","63","6","4","42","14","32","-42","7","-1","24","-30","12","-36","-22","0","18","10","-3","69","7","21","27","-7","12","72","-24","24","-9","-26","4","12","-1","-2","-30","-8","10","-21","5","24","42","0","12","18","-9","-33","36","-1","-5","36","-20","12","18","1","-1","18","18","49","6","0","42","-12","-1","1","30","36","-21","84","-3","12","-6","-8","-4","12","-14","18","-27","-9","-6","15","2","-36","21","4","-6","-24","-4","12","-9","8","-18","126","3","2","-42","-28","-25","-48","2","15","15","-35","-26","9","-23","-16","33","8","21","60","15","4","-12","-10","-13","66","-4","60","12","-27","-9","18","30","10","63","-42","-9","54","-1","-10","-54","-14","21","-12","19","-10","9","2","14","-84","-36","20","-21","-18","-18","-72","-15","-16","-6","12","-15","-3","22","-7","-6","19","18","-27","-4","-28","-15","43","-22","-18","20","6","36","32","7","-36","-10","36","-45","-12","-7","-6","21","-2","3","-24","4","24","42","1","-9","27","-24","36","-6","-48","3","7","-21","-42","-9","18","-51","-4","3","66","14","-42","24","5","-24","-21","12","12","18","42","-28","-63","6","-18","12","-28","-23","6","-14","11","-54","-30","10","-30","-24","-12","6","28","5","72","-10","-12","-6","4","-30","18","30","-24","9","36","7","-24","-21","-2","21","8","3","-36","-6","4","-30","-24","-36","9","-3","20","-24","2","-1","-90","-42","42","30","25","-6","45","-5","-21","-9","20","30","24","4","23","-24","-2","10","-42","-7","-28","-42","21","5","12","6","3","-54","-15","-4","18","-27","-39","45","9","-28","96","-5","-42","-21","-12","-21","48","8","1","12","14","8","-66","-3","-3","-36","-34","-42","-9","9","52","63","1","12","27","16","-8","-36","18","-3","-72","-26","-35","-6","70","18","12","-33","-22","3","37","-20","-60","-6","19","-6","-3","-6","15","-22","4","-63","28","-12","36","4","-84","-9","-7","7","72","-35","-43","15","-12","-18","-60","-40","-21","108","20","2","-3","4","23","-54","24","3","9","12","-4","42","24","2","-3","21","49","-60","21","24","-63","21","-10","21","-6","42","-12","1","-14","12","-30","6","-42","8","30","0","10","-28","-18","-5","9","-6","36","6","42","10","-20","-54","23","49","-12","12","16","18","33","25","-54","14","24","3","-53","31","-63","-3"],"lmfdb":"agrees","curve":{"cremona":"415a1","lmfdb":"415.a","ainvs":[1,-1,0,-109,-412],"rank":0,"torsion":1},"space":"415.2.a","level":415,"weight":2,"T":[[2,1],[3,3]],"status":"proven","derived":{"al":[[5,-1],[83,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0},"url":"https://sagebrush.space/atlas/mf/415.2.a.a"}