LMFDB - Hilbert modular form data

Formats: - HTML - YAML - JSON - 2026-03-19T10:54:13.338869

Column	Type
deg	smallint
dimension	integer
disc	bigint
field_bad_primes	integer[]
field_label	text
is_CM	text
is_base_change	text
label	text
label_nsuffix	smallint
label_suffix	text
level_bad_primes	integer[]
level_ideal	text
level_label	text
level_norm	integer
parallel_weight	smallint
short_label	text
weight	text

hmf_forms • Show schema

{'deg': 4, 'dimension': 7, 'disc': 18625, 'field_bad_primes': [5, 149], 'field_label': '4.4.18625.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.18625.1-9.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [3], 'level_ideal': '[9, 3, 1/6*w^3 - 7/3*w + 13/6]', 'level_label': '9.1', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.1-b', 'weight': '[2, 2, 2, 2]'}

Column	Type
AL_eigenvalues	jsonb
hecke_eigenvalues	jsonb
hecke_polynomial	text
label	text

hmf_hecke • Show schema

{'AL_eigenvalues': [['[9, 3, 1/6*w^3 - 7/3*w + 13/6]', -1]], 'hecke_eigenvalues': ['-7/139*e^6 + 13/139*e^5 + 120/139*e^4 - 236/139*e^3 - 401/139*e^2 + 1018/139*e - 685/139', 'e', '-15/278*e^6 + 4/139*e^5 + 277/278*e^4 - 94/139*e^3 - 658/139*e^2 + 851/278*e + 110/139', 1, '35/278*e^6 + 37/139*e^5 - 461/278*e^4 - 383/139*e^3 + 794/139*e^2 + 1721/278*e - 720/139', '7/139*e^6 - 13/139*e^5 - 120/139*e^4 + 236/139*e^3 + 401/139*e^2 - 1157/139*e + 546/139', '13/278*e^6 - 22/139*e^5 - 203/278*e^4 + 517/139*e^3 + 283/139*e^2 - 5167/278*e + 1341/139', '113/278*e^6 + 322/139*e^5 - 567/278*e^4 - 3397/139*e^3 - 566/139*e^2 + 15199/278*e - 3099/139', '29/278*e^6 - 156/139*e^5 - 1073/278*e^4 + 1998/139*e^3 + 2866/139*e^2 - 13451/278*e + 1826/139', '18/139*e^6 + 185/139*e^5 + 168/139*e^4 - 1915/139*e^3 - 2424/139*e^2 + 4372/139*e + 570/139', '-187/278*e^6 - 293/139*e^5 + 1637/278*e^4 + 2368/139*e^3 - 799/139*e^2 - 3087/278*e - 1455/139', '57/278*e^6 + 235/139*e^5 + 115/278*e^4 - 2534/139*e^3 - 1753/139*e^2 + 12779/278*e - 1669/139', '53/139*e^6 + 120/139*e^5 - 710/139*e^4 - 1152/139*e^3 + 2361/139*e^2 + 1645/139*e - 314/139', '112/139*e^6 + 348/139*e^5 - 1225/139*e^4 - 3174/139*e^3 + 3497/139*e^2 + 4562/139*e - 2384/139', '31/278*e^6 - 138/139*e^5 - 1147/278*e^4 + 1714/139*e^3 + 3241/139*e^2 - 10803/278*e + 931/139', '15/139*e^6 + 131/139*e^5 - 138/139*e^4 - 1897/139*e^3 + 621/139*e^2 + 6794/139*e - 3834/139', '-97/139*e^6 - 356/139*e^5 + 948/139*e^4 + 3362/139*e^3 - 2320/139*e^2 - 5413/139*e + 3276/139', '-13/278*e^6 - 256/139*e^5 - 909/278*e^4 + 2958/139*e^3 + 3748/139*e^2 - 15405/278*e + 605/139', '-227/278*e^6 - 375/139*e^5 + 2283/278*e^4 + 3461/139*e^3 - 2600/139*e^2 - 10177/278*e + 1850/139', '38/139*e^6 + 267/139*e^5 - 155/139*e^4 - 2869/139*e^3 - 345/139*e^2 + 6249/139*e - 3430/139', '-53/278*e^6 + 79/139*e^5 + 1127/278*e^4 - 1231/139*e^3 - 2640/139*e^2 + 9475/278*e - 1650/139', '25/278*e^6 - 53/139*e^5 - 647/278*e^4 + 759/139*e^3 + 1838/139*e^2 - 4847/278*e + 141/139', '-126/139*e^6 - 461/139*e^5 + 1187/139*e^4 + 4509/139*e^3 - 2353/139*e^2 - 8364/139*e + 3516/139', '31/278*e^6 - 138/139*e^5 - 869/278*e^4 + 1853/139*e^3 + 2268/139*e^2 - 11637/278*e + 375/139', '135/139*e^6 + 484/139*e^5 - 1242/139*e^4 - 4424/139*e^3 + 2114/139*e^2 + 5963/139*e - 1980/139', '69/278*e^6 + 65/139*e^5 - 885/278*e^4 - 207/139*e^3 + 1470/139*e^2 - 4415/278*e + 328/139', '-145/139*e^6 - 525/139*e^5 + 1334/139*e^4 + 4762/139*e^3 - 2389/139*e^2 - 6137/139*e + 1756/139', '-17/278*e^6 + 125/139*e^5 + 629/278*e^4 - 1617/139*e^3 - 1450/139*e^2 + 10435/278*e - 1914/139', '53/278*e^6 - 218/139*e^5 - 1683/278*e^4 + 2899/139*e^3 + 4308/139*e^2 - 20317/278*e + 2345/139', '255/278*e^6 + 349/139*e^5 - 3041/278*e^4 - 3267/139*e^3 + 4653/139*e^2 + 8607/278*e - 2565/139', '55/139*e^6 + 573/139*e^5 + 189/139*e^4 - 6585/139*e^3 - 3700/139*e^2 + 17637/139*e - 5440/139', '5/139*e^6 - 49/139*e^5 - 46/139*e^4 + 1082/139*e^3 - 210/139*e^2 - 4917/139*e + 3726/139', '-57/278*e^6 + 43/139*e^5 + 997/278*e^4 - 663/139*e^3 - 1861/139*e^2 + 4457/278*e - 694/139', '-56/139*e^6 - 313/139*e^5 + 404/139*e^4 + 3394/139*e^3 - 706/139*e^2 - 8119/139*e + 4250/139', '26/139*e^6 - 88/139*e^5 - 545/139*e^4 + 1373/139*e^3 + 2383/139*e^2 - 5747/139*e + 360/139', '-135/139*e^6 - 206/139*e^5 + 1937/139*e^4 + 1644/139*e^3 - 7118/139*e^2 - 264/139*e + 2536/139', '38/139*e^6 + 128/139*e^5 - 294/139*e^4 - 1062/139*e^3 - 67/139*e^2 + 1523/139*e + 1296/139', '-10/139*e^6 - 41/139*e^5 + 231/139*e^4 + 477/139*e^3 - 1526/139*e^2 - 452/139*e + 2556/139', '108/139*e^6 + 276/139*e^5 - 1355/139*e^4 - 2316/139*e^3 + 4777/139*e^2 + 1768/139*e - 2974/139', '93/139*e^6 + 562/139*e^5 - 522/139*e^4 - 6118/139*e^3 - 570/139*e^2 + 14017/139*e - 5534/139', '-143/278*e^6 - 175/139*e^5 + 1955/278*e^4 + 1680/139*e^3 - 3947/139*e^2 - 5435/278*e + 3736/139', '-131/278*e^6 - 345/139*e^5 + 677/278*e^4 + 3590/139*e^3 + 666/139*e^2 - 16513/278*e + 1980/139', '255/278*e^6 + 349/139*e^5 - 2763/278*e^4 - 3128/139*e^3 + 3402/139*e^2 + 8051/278*e - 1870/139', '-78/139*e^6 - 292/139*e^5 + 523/139*e^4 + 2275/139*e^3 + 774/139*e^2 - 829/139*e - 3304/139', '183/278*e^6 + 118/139*e^5 - 2879/278*e^4 - 827/139*e^3 + 5748/139*e^2 - 2765/278*e - 369/139', '42/139*e^6 + 61/139*e^5 - 442/139*e^4 - 252/139*e^3 + 877/139*e^2 - 1104/139*e - 60/139', '-83/139*e^6 - 243/139*e^5 + 986/139*e^4 + 2305/139*e^3 - 3186/139*e^2 - 3835/139*e - 80/139', '163/139*e^6 + 432/139*e^5 - 1861/139*e^4 - 3758/139*e^3 + 5247/139*e^2 + 4115/139*e - 2020/139', '2/139*e^6 - 103/139*e^5 - 74/139*e^4 + 1239/139*e^3 + 55/139*e^2 - 2217/139*e + 2380/139', '90/139*e^6 + 369/139*e^5 - 828/139*e^4 - 3459/139*e^3 + 1502/139*e^2 + 4346/139*e - 1320/139', '-163/278*e^6 - 216/139*e^5 + 1583/278*e^4 + 1462/139*e^3 - 1442/139*e^2 + 2001/278*e - 1770/139', '64/139*e^6 + 40/139*e^5 - 978/139*e^4 + 311/139*e^3 + 3289/139*e^2 - 5475/139*e + 2768/139', '-61/278*e^6 + 285/139*e^5 + 1701/278*e^4 - 4265/139*e^3 - 4001/139*e^2 + 31965/278*e - 5437/139', '-119/278*e^6 + 41/139*e^5 + 1901/278*e^4 - 1589/139*e^3 - 3339/139*e^2 + 20503/278*e - 4919/139', '69/278*e^6 + 482/139*e^5 + 783/278*e^4 - 5767/139*e^3 - 4229/139*e^2 + 33115/278*e - 4954/139', '-116/139*e^6 - 420/139*e^5 + 1234/139*e^4 + 4588/139*e^3 - 3607/139*e^2 - 10970/139*e + 7076/139', '-57/139*e^6 + 225/139*e^5 + 1414/139*e^4 - 3411/139*e^3 - 7058/139*e^2 + 13631/139*e - 3334/139', '-125/278*e^6 - 430/139*e^5 + 177/278*e^4 + 4267/139*e^3 + 1930/139*e^2 - 17465/278*e + 3048/139', '-15/278*e^6 - 274/139*e^5 - 835/278*e^4 + 2964/139*e^3 + 3234/139*e^2 - 13605/278*e + 1083/139', '14/139*e^6 - 26/139*e^5 - 101/139*e^4 + 889/139*e^3 + 246/139*e^2 - 4260/139*e + 258/139', '-53/278*e^6 - 60/139*e^5 + 571/278*e^4 + 437/139*e^3 - 833/139*e^2 - 1645/278*e + 713/139', '30/139*e^6 + 401/139*e^5 + 280/139*e^4 - 4211/139*e^3 - 3067/139*e^2 + 9140/139*e - 2942/139', '-229/278*e^6 - 393/139*e^5 + 1801/278*e^4 + 3328/139*e^3 - 751/139*e^2 - 7265/278*e + 1633/139', '369/278*e^6 + 680/139*e^5 - 3367/278*e^4 - 6806/139*e^3 + 3093/139*e^2 + 27493/278*e - 5069/139', '-64/139*e^6 - 318/139*e^5 + 283/139*e^4 + 3164/139*e^3 + 1993/139*e^2 - 6062/139*e - 544/139', '-125/278*e^6 - 13/139*e^5 + 1567/278*e^4 - 876/139*e^3 - 2379/139*e^2 + 13393/278*e - 705/139', '15/278*e^6 - 282/139*e^5 - 1111/278*e^4 + 4264/139*e^3 + 3438/139*e^2 - 31709/278*e + 5450/139', '-395/278*e^6 - 497/139*e^5 + 4329/278*e^4 + 3965/139*e^3 - 5605/139*e^2 - 5205/278*e + 163/139', '23/139*e^6 + 414/139*e^5 + 539/139*e^4 - 4447/139*e^3 - 4997/139*e^2 + 10853/139*e - 2654/139', '-92/139*e^6 - 544/139*e^5 + 763/139*e^4 + 6112/139*e^3 - 2252/139*e^2 - 15890/139*e + 7280/139', '164/139*e^6 + 450/139*e^5 - 1759/139*e^4 - 3208/139*e^3 + 4927/139*e^2 - 260/139*e - 2220/139', '59/139*e^6 + 228/139*e^5 - 376/139*e^4 - 2161/139*e^3 - 254/139*e^2 + 3890/139*e - 3460/139', '209/278*e^6 + 491/139*e^5 - 1339/278*e^4 - 4936/139*e^3 - 358/139*e^2 + 21095/278*e - 4220/139', '130/139*e^6 + 255/139*e^5 - 1474/139*e^4 - 1614/139*e^3 + 4409/139*e^2 - 1491/139*e - 3760/139', '-128/139*e^6 - 636/139*e^5 + 1122/139*e^4 + 7162/139*e^3 - 2408/139*e^2 - 17406/139*e + 8920/139', '-215/278*e^6 + 11/139*e^5 + 3507/278*e^4 - 1162/139*e^3 - 6744/139*e^2 + 17665/278*e - 3242/139', '280/139*e^6 + 870/139*e^5 - 2715/139*e^4 - 7518/139*e^3 + 5476/139*e^2 + 8625/139*e - 2902/139', '-65/139*e^6 - 475/139*e^5 + 320/139*e^4 + 5811/139*e^3 + 645/139*e^2 - 17255/139*e + 4938/139', '74/139*e^6 + 359/139*e^5 - 375/139*e^4 - 3780/139*e^3 - 884/139*e^2 + 9850/139*e - 3402/139', '-216/139*e^6 - 552/139*e^5 + 2432/139*e^4 + 4771/139*e^3 - 6913/139*e^2 - 5899/139*e + 2890/139', '-1/2*e^6 - 5*e^5 - 3/2*e^4 + 53*e^3 + 31*e^2 - 237/2*e + 30', '52/139*e^6 - 315/139*e^5 - 1229/139*e^4 + 4970/139*e^3 + 5183/139*e^2 - 20390/139*e + 9060/139', '-127/278*e^6 - 448/139*e^5 + 251/278*e^4 + 5107/139*e^3 + 2528/139*e^2 - 25395/278*e + 2970/139', '308/139*e^6 + 957/139*e^5 - 3473/139*e^4 - 9354/139*e^3 + 10138/139*e^2 + 16368/139*e - 8780/139', '-373/139*e^6 - 1154/139*e^5 + 3932/139*e^4 + 10856/139*e^3 - 10049/139*e^2 - 17499/139*e + 9270/139', '-217/139*e^6 - 987/139*e^5 + 1774/139*e^4 + 10059/139*e^3 - 2423/139*e^2 - 20150/139*e + 7538/139', '211/278*e^6 + 231/139*e^5 - 2247/278*e^4 - 1606/139*e^3 + 3075/139*e^2 - 165/278*e - 2752/139', '196/139*e^6 + 609/139*e^5 - 2109/139*e^4 - 5485/139*e^3 + 5251/139*e^2 + 6802/139*e - 1670/139', '441/278*e^6 + 633/139*e^5 - 4363/278*e^4 - 5076/139*e^3 + 3388/139*e^2 + 4393/278*e + 4550/139', '210/139*e^6 + 1000/139*e^5 - 1376/139*e^4 - 9878/139*e^3 - 341/139*e^2 + 19500/139*e - 5304/139', '213/278*e^6 + 666/139*e^5 - 1209/278*e^4 - 7172/139*e^3 - 581/139*e^2 + 31395/278*e - 7539/139', '269/278*e^6 + 475/139*e^5 - 2447/278*e^4 - 4282/139*e^3 + 2830/139*e^2 + 13799/278*e - 6745/139', '-130/139*e^6 - 811/139*e^5 + 223/139*e^4 + 8147/139*e^3 + 4904/139*e^2 - 17969/139*e + 2370/139', '98/139*e^6 + 374/139*e^5 - 707/139*e^4 - 3368/139*e^3 + 332/139*e^2 + 4791/139*e - 2920/139', '94/139*e^6 + 441/139*e^5 - 837/139*e^4 - 4873/139*e^3 + 1612/139*e^2 + 11310/139*e - 6290/139', '140/139*e^6 + 157/139*e^5 - 1983/139*e^4 - 840/139*e^3 + 7325/139*e^2 - 2290/139*e - 3814/139', '119/278*e^6 + 376/139*e^5 - 233/278*e^4 - 4110/139*e^3 - 2221/139*e^2 + 22587/278*e - 1614/139', '-141/278*e^6 - 574/139*e^5 + 213/278*e^4 + 6261/139*e^3 + 1988/139*e^2 - 30031/278*e + 3675/139', '-148/139*e^6 - 718/139*e^5 + 1167/139*e^4 + 7699/139*e^3 - 1568/139*e^2 - 18032/139*e + 8750/139', '80/139*e^6 + 50/139*e^5 - 1292/139*e^4 - 202/139*e^3 + 5119/139*e^2 - 1249/139*e - 1544/139', '153/139*e^6 + 530/139*e^5 - 1769/139*e^4 - 5783/139*e^3 + 5945/139*e^2 + 12837/139*e - 9194/139', '322/139*e^6 + 931/139*e^5 - 3574/139*e^4 - 8604/139*e^3 + 10384/139*e^2 + 11969/139*e - 8800/139', '71/139*e^6 - 112/139*e^5 - 1237/139*e^4 + 2493/139*e^3 + 4385/139*e^2 - 13304/139*e + 3870/139', '-55/278*e^6 - 495/139*e^5 - 1023/278*e^4 + 5864/139*e^3 + 4491/139*e^2 - 33761/278*e + 4805/139', '221/278*e^6 + 599/139*e^5 - 2061/278*e^4 - 6779/139*e^3 + 3421/139*e^2 + 33647/278*e - 10285/139', '171/278*e^6 + 983/139*e^5 + 901/278*e^4 - 11355/139*e^3 - 6510/139*e^2 + 61967/278*e - 12930/139', '-123/139*e^6 - 685/139*e^5 + 1076/139*e^4 + 7966/139*e^3 - 3313/139*e^2 - 23157/139*e + 12090/139', '2*e^3 + 3*e^2 - 10*e - 28', '30/139*e^6 - 294/139*e^5 - 1110/139*e^4 + 3434/139*e^3 + 7080/139*e^2 - 8652/139*e - 2664/139', '-135/139*e^6 - 484/139*e^5 + 964/139*e^4 + 4146/139*e^3 + 388/139*e^2 - 4990/139*e - 522/139', '64/139*e^6 - 99/139*e^5 - 1117/139*e^4 + 2118/139*e^3 + 4262/139*e^2 - 10340/139*e + 1656/139', '-299/139*e^6 - 1073/139*e^5 + 2723/139*e^4 + 10134/139*e^3 - 5234/139*e^2 - 17379/139*e + 5590/139', '-101/278*e^6 - 75/139*e^5 + 1791/278*e^4 + 859/139*e^3 - 3995/139*e^2 - 3203/278*e + 1065/139', '-597/278*e^6 - 647/139*e^5 + 6521/278*e^4 + 3876/139*e^3 - 7479/139*e^2 + 14521/278*e - 6325/139', '115/278*e^6 + 201/139*e^5 - 919/278*e^4 - 2013/139*e^3 + 504/139*e^2 + 8117/278*e - 3160/139', '-406/139*e^6 - 1331/139*e^5 + 3902/139*e^4 + 11888/139*e^3 - 7551/139*e^2 - 14765/139*e + 3638/139', '-155/278*e^6 + 134/139*e^5 + 3233/278*e^4 - 2454/139*e^3 - 7726/139*e^2 + 23435/278*e - 902/139', '373/139*e^6 + 1571/139*e^5 - 3098/139*e^4 - 15582/139*e^3 + 4489/139*e^2 + 28758/139*e - 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3106/139*e^4 - 11248/139*e^3 + 2162/139*e^2 + 12214/139*e - 4/139', '-423/139*e^6 - 1498/139*e^5 + 3975/139*e^4 + 14631/139*e^3 - 7671/139*e^2 - 27960/139*e + 9818/139', '23/139*e^6 - 142/139*e^5 - 990/139*e^4 + 1530/139*e^3 + 7513/139*e^2 - 4020/139*e - 5434/139', '-185/139*e^6 - 967/139*e^5 + 1424/139*e^4 + 10423/139*e^3 - 987/139*e^2 - 21984/139*e + 2250/139', '-133/139*e^6 - 31/139*e^5 + 2141/139*e^4 - 1009/139*e^3 - 8175/139*e^2 + 11419/139*e + 1580/139', '525/278*e^6 + 138/139*e^5 - 8583/278*e^4 + 1066/139*e^3 + 17609/139*e^2 - 31175/278*e + 6575/139', '-83/139*e^6 + 869/139*e^5 + 2793/139*e^4 - 11873/139*e^3 - 14167/139*e^2 + 41896/139*e - 12590/139', '612/139*e^6 + 2537/139*e^5 - 4991/139*e^4 - 24522/139*e^3 + 5571/139*e^2 + 42452/139*e - 13424/139', '233/139*e^6 - 254/139*e^5 - 4312/139*e^4 + 4718/139*e^3 + 18709/139*e^2 - 21772/139*e + 5386/139', '-7/139*e^6 + 13/139*e^5 + 120/139*e^4 - 375/139*e^3 - 679/139*e^2 - 94/139*e + 1956/139', '-63/278*e^6 - 428/139*e^5 - 449/278*e^4 + 5054/139*e^3 + 3269/139*e^2 - 25171/278*e + 1991/139', '423/139*e^6 + 1220/139*e^5 - 4253/139*e^4 - 9766/139*e^3 + 7671/139*e^2 + 3496/139*e + 7696/139', '304/139*e^6 + 1441/139*e^5 - 2352/139*e^4 - 14334/139*e^3 + 3495/139*e^2 + 28169/139*e - 12984/139', '-303/278*e^6 - 920/139*e^5 + 925/278*e^4 + 9805/139*e^3 + 4556/139*e^2 - 44915/278*e + 10840/139', '-32/139*e^6 - 159/139*e^5 - 623/139*e^4 + 470/139*e^3 + 8572/139*e^2 + 4892/139*e - 11670/139', '-270/139*e^6 - 2080/139*e^5 + 816/139*e^4 + 23582/139*e^3 + 5363/139*e^2 - 61410/139*e + 25088/139', '-180/139*e^6 - 1155/139*e^5 + 683/139*e^4 + 12478/139*e^3 + 4502/139*e^2 - 29820/139*e + 7088/139', '-22/139*e^6 - 118/139*e^5 - 159/139*e^4 - 7/139*e^3 + 2592/139*e^2 + 7012/139*e - 3940/139', '9/139*e^6 - 811/139*e^5 - 2140/139*e^4 + 8147/139*e^3 + 16163/139*e^2 - 15606/139*e - 8750/139', '-403/278*e^6 - 291/139*e^5 + 6571/278*e^4 + 2460/139*e^3 - 15167/139*e^2 - 6067/278*e + 10415/139', '-7/278*e^6 - 341/139*e^5 - 853/278*e^4 + 5164/139*e^3 + 1954/139*e^2 - 42767/278*e + 9735/139', '-165/278*e^6 - 1068/139*e^5 - 2235/278*e^4 + 11059/139*e^3 + 13612/139*e^2 - 45961/278*e - 5184/139', '21/278*e^6 - 228/139*e^5 - 1611/278*e^4 + 1188/139*e^3 + 5814/139*e^2 + 9595/278*e - 7104/139', '-1283/278*e^6 - 2234/139*e^5 + 11609/278*e^4 + 20112/139*e^3 - 9753/139*e^2 - 54183/278*e + 8621/139', '223/278*e^6 + 617/139*e^5 - 745/278*e^4 - 6229/139*e^3 - 3988/139*e^2 + 25453/278*e - 199/139', '-275/278*e^6 - 946/139*e^5 - 389/278*e^4 + 9165/139*e^3 + 8138/139*e^2 - 38145/278*e + 4148/139', '-317/139*e^6 - 1119/139*e^5 + 3250/139*e^4 + 10381/139*e^3 - 9065/139*e^2 - 14940/139*e + 12248/139', '65/139*e^6 + 614/139*e^5 - 42/139*e^4 - 6784/139*e^3 - 2591/139*e^2 + 14753/139*e - 8274/139', '93/139*e^6 + 6/139*e^5 - 1773/139*e^4 + 693/139*e^3 + 8743/139*e^2 - 5026/139*e - 2754/139', '252/139*e^6 - 190/139*e^5 - 4181/139*e^4 + 5577/139*e^3 + 14714/139*e^2 - 34424/139*e + 17710/139', '-73/139*e^6 - 341/139*e^5 + 199/139*e^4 + 2523/139*e^3 + 2371/139*e^2 + 92/139*e - 690/139', '-226/139*e^6 + 519/139*e^5 + 4748/139*e^4 - 8374/139*e^3 - 22200/139*e^2 + 34932/139*e - 4284/139', '421/278*e^6 + 1009/139*e^5 - 2789/278*e^4 - 11132/139*e^3 - 640/139*e^2 + 55753/278*e - 12354/139', '412/139*e^6 + 605/139*e^5 - 5931/139*e^4 - 3445/139*e^3 + 23701/139*e^2 - 7732/139*e - 10120/139', '497/139*e^6 + 2274/139*e^5 - 3655/139*e^4 - 23137/139*e^3 + 2617/139*e^2 + 50320/139*e - 18780/139'], 'hecke_polynomial': 'x^7 + 4*x^6 - 11*x^5 - 44*x^4 + 42*x^3 + 105*x^2 - 110*x + 20', 'label': '4.4.18625.1-9.1-b'}

Column	Type
degree	smallint
discriminant	bigint
ideals	jsonb
label	text
narrow_class_no	smallint
primes	jsonb

hmf_fields • Show schema

{'degree': 4, 'discriminant': 18625, 'ideals': ['[1, 1, 1]', '[4, 2, 1/6*w^3 - 7/3*w - 17/6]', '[4, 2, w - 3]', '[5, 5, -1/6*w^3 + w^2 + 1/3*w - 25/6]', '[9, 3, 1/6*w^3 - 7/3*w + 13/6]', '[9, 3, -w - 2]', '[11, 11, -1/6*w^3 + 7/3*w + 11/6]', '[11, 11, -w + 2]', '[16, 2, 2]', '[16, 4, -1/6*w^3 + 1/3*w + 5/6]', '[16, 4, 1/3*w^3 - 11/3*w - 2/3]', '[20, 10, w + 1]', '[20, 10, -1/6*w^3 + 7/3*w - 7/6]', '[25, 5, -1/3*w^3 + 8/3*w + 2/3]', '[36, 6, -1/6*w^3 + 7/3*w + 5/6]', '[36, 6, 1/3*w^3 + w^2 - 11/3*w - 35/3]', '[36, 6, -w^2 + w + 3]', '[36, 6, w - 1]', '[41, 41, -w]', '[41, 41, 1/6*w^3 - 7/3*w + 1/6]', '[44, 22, 1/3*w^3 - 11/3*w + 4/3]', '[44, 22, 1/3*w^3 - 11/3*w - 8/3]', '[44, 22, -1/6*w^3 + 1/3*w + 17/6]', '[44, 22, 1/6*w^3 - 1/3*w + 7/6]', '[45, 15, -1/6*w^3 + 7/3*w + 23/6]', '[45, 15, -w + 4]', '[55, 55, 1/3*w^3 - 5/3*w + 1/3]', '[55, 55, 1/2*w^3 - 5*w + 1/2]', '[59, 59, -1/6*w^3 + 1/3*w + 23/6]', '[59, 59, -1/3*w^3 + 11/3*w + 11/3]', '[61, 61, -5/3*w^3 - 3*w^2 + 46/3*w + 79/3]', '[61, 61, 5/6*w^3 + w^2 - 23/3*w - 55/6]', '[61, 61, w^3 + 2*w^2 - 9*w - 17]', '[61, 61, -1/6*w^3 + 10/3*w + 35/6]', '[64, 4, 1/3*w^3 - 14/3*w - 17/3]', '[64, 4, 2*w - 6]', '[64, 8, 1/6*w^3 + w^2 - 4/3*w - 59/6]', '[64, 8, -w^2 + 5]', '[71, 71, -1/2*w^3 + 2*w^2 + 4*w - 33/2]', '[71, 71, 1/6*w^3 - w^2 - 4/3*w + 67/6]', '[79, 79, 1/2*w^3 - 3*w + 1/2]', '[79, 79, -2/3*w^3 + 19/3*w - 2/3]', '[80, 10, -1/3*w^3 + 2*w^2 + 2/3*w - 25/3]', '[80, 20, -1/3*w^3 + w^2 + 5/3*w - 19/3]', '[80, 20, 2/3*w^3 + w^2 - 19/3*w - 25/3]', '[81, 3, 3]', '[81, 9, -1/3*w^3 + 2*w^2 + 2/3*w - 28/3]', '[81, 9, w^3 + 2*w^2 - 10*w - 20]', '[89, 89, 1/2*w^3 + w^2 - 5*w - 15/2]', '[89, 89, 1/3*w^3 - 11/3*w + 7/3]', '[99, 33, -w^2 + 2*w + 2]', '[99, 33, 1/6*w^3 + w^2 - 4/3*w - 65/6]', '[99, 33, w^2 - 4]', '[99, 33, 1/2*w^3 + w^2 - 6*w - 25/2]', '[100, 10, 7/6*w^3 + 2*w^2 - 31/3*w - 107/6]', '[100, 10, 2/3*w^3 - 2*w^2 - 13/3*w + 35/3]', '[101, 101, -5/6*w^3 - w^2 + 23/3*w + 61/6]', '[101, 101, 1/2*w^3 - w^2 - 3*w + 9/2]', '[109, 109, 1/2*w^3 - w^2 - 4*w + 11/2]', '[109, 109, -2/3*w^3 - w^2 + 16/3*w + 28/3]', '[121, 11, 1/2*w^3 - 4*w - 3/2]', '[121, 11, -1/2*w^3 + 4*w + 1/2]', '[121, 121, 1/6*w^3 - 10/3*w + 25/6]', '[121, 121, 1/6*w^3 - 10/3*w - 23/6]', '[125, 5, -1/2*w^3 + w^2 + w - 1/2]', '[131, 131, 2*w - 7]', '[131, 131, -7/6*w^3 - 2*w^2 + 28/3*w + 89/6]', '[139, 139, -1/6*w^3 + w^2 + 4/3*w - 31/6]', '[139, 139, 1/3*w^3 + w^2 - 8/3*w - 29/3]', '[144, 6, 1/3*w^3 - 14/3*w + 13/3]', '[144, 6, -2*w - 4]', '[144, 12, -1/3*w^3 + w^2 - 1/3*w + 2/3]', '[144, 12, -1/3*w^3 + 5/3*w - 4/3]', '[144, 12, 1/2*w^3 - 5*w + 3/2]', '[144, 12, -w^3 - 2*w^2 + 9*w + 18]', '[149, 149, 1/6*w^3 - 2*w^2 + 5/3*w + 37/6]', '[151, 151, -7/6*w^3 + 3*w^2 + 28/3*w - 133/6]', '[151, 151, 5/3*w^3 + 3*w^2 - 40/3*w - 67/3]', '[164, 82, 1/2*w^3 + 2*w^2 - 5*w - 41/2]', '[164, 82, 2/3*w^3 - 2*w^2 - 13/3*w + 41/3]', '[164, 82, -7/6*w^3 - 2*w^2 + 31/3*w + 95/6]', '[164, 82, -2*w^2 + w + 9]', '[169, 13, -1/6*w^3 - 2/3*w + 29/6]', '[169, 13, 7/6*w^3 - 4*w^2 - 19/3*w + 139/6]', '[176, 22, -1/3*w^3 + 14/3*w + 11/3]', '[176, 22, -2*w + 4]', '[176, 44, 2/3*w^3 - w^2 - 10/3*w + 11/3]', '[176, 44, 1/3*w^3 - w^2 - 11/3*w + 37/3]', '[176, 44, -1/3*w^3 - w^2 + 5/3*w + 8/3]', '[176, 44, -7/6*w^3 - w^2 + 34/3*w + 65/6]', '[180, 30, 1/3*w^3 - w^2 - 8/3*w + 16/3]', '[180, 30, 1/2*w^3 - w^2 - 2*w + 9/2]', '[180, 30, -w^3 - w^2 + 10*w + 10]', '[180, 30, 1/2*w^3 + w^2 - 4*w - 19/2]', '[181, 181, -2/3*w^3 + 13/3*w + 10/3]', '[181, 181, 5/6*w^3 - 23/3*w - 19/6]', '[191, 191, 5/6*w^3 + w^2 - 32/3*w - 97/6]', '[191, 191, w^3 - 9*w - 5]', '[191, 191, -w^2 + 4*w - 2]', '[191, 191, 5/6*w^3 + w^2 - 17/3*w - 43/6]', '[199, 199, 1/2*w^3 - 2*w - 7/2]', '[199, 199, 7/6*w^3 - 5*w^2 - 7/3*w + 109/6]', '[205, 205, 3/2*w^3 + 2*w^2 - 15*w - 41/2]', '[205, 205, -2/3*w^3 + 2*w^2 + 7/3*w - 26/3]', '[211, 211, -1/6*w^3 + w^2 + 7/3*w - 79/6]', '[211, 211, 1/2*w^3 + 2*w^2 - 6*w - 37/2]', '[220, 110, -w^2 + w + 2]', '[220, 110, -1/3*w^3 - w^2 + 11/3*w + 38/3]', '[220, 110, -5/3*w^3 - 3*w^2 + 49/3*w + 88/3]', '[220, 110, -2/3*w^3 + 3*w^2 + 7/3*w - 44/3]', '[225, 15, -1/2*w^3 + 2*w^2 + 3*w - 29/2]', '[225, 15, w^3 + 2*w^2 - 9*w - 15]', '[229, 229, -1/2*w^3 + 5*w - 5/2]', '[229, 229, 1/2*w^3 - 2*w^2 - 2*w + 23/2]', '[229, 229, 1/6*w^3 + w^2 - 10/3*w - 53/6]', '[229, 229, -7/6*w^3 - 2*w^2 + 34/3*w + 107/6]', '[236, 118, 1/6*w^3 - 7/3*w - 29/6]', '[236, 118, -w^3 - w^2 + 11*w + 13]', '[236, 118, 1/3*w^3 - w^2 + 1/3*w + 4/3]', '[236, 118, w - 5]', '[239, 239, 2*w^3 + 3*w^2 - 22*w - 36]', '[239, 239, -7/3*w^3 - 3*w^2 + 74/3*w + 113/3]', '[241, 241, -1/3*w^3 - w^2 + 2/3*w + 11/3]', '[241, 241, -1/2*w^3 + w^2 + 6*w - 23/2]', '[244, 122, -2/3*w^3 + 19/3*w - 5/3]', '[244, 122, 1/3*w^3 - w^2 - 11/3*w + 19/3]', '[244, 122, -2/3*w^3 - w^2 + 13/3*w + 25/3]', '[244, 122, 2/3*w^3 + w^2 - 19/3*w - 22/3]', '[244, 122, -25/6*w^3 - 7*w^2 + 118/3*w + 395/6]', '[244, 122, 1/3*w^3 + w^2 - 5/3*w - 26/3]', '[244, 122, -2/3*w^3 + w^2 + 19/3*w - 20/3]', '[244, 122, 1/2*w^3 - 3*w + 3/2]', '[256, 4, 4]', '[256, 8, -1/3*w^3 + 2/3*w + 5/3]', '[256, 8, 2/3*w^3 - 22/3*w - 4/3]', '[256, 16, 1/6*w^3 - 13/3*w + 43/6]', '[256, 16, 1/3*w^3 - 17/3*w - 20/3]', '[271, 271, -5/6*w^3 - w^2 + 20/3*w + 49/6]', '[271, 271, 1/6*w^3 - 1/3*w - 35/6]', '[275, 55, -5/6*w^3 - 2*w^2 + 23/3*w + 103/6]', '[275, 55, -1/3*w^3 + 2*w^2 + 5/3*w - 37/3]', '[281, 281, -1/6*w^3 - w^2 + 7/3*w + 11/6]', '[281, 281, -w^3 + 9*w - 1]', '[281, 281, -1/2*w^3 + 8*w + 19/2]', '[281, 281, w^3 - 4*w^2 - 4*w + 20]', '[284, 142, 4/3*w^3 - 41/3*w - 11/3]', '[284, 142, -4/3*w^3 + 4*w^2 + 41/3*w - 121/3]', '[284, 142, -w^2 + w + 11]', '[284, 142, 7/6*w^3 + w^2 - 40/3*w - 101/6]', '[295, 295, 1/3*w^3 - 17/3*w + 19/3]', '[295, 295, 1/6*w^3 - 13/3*w - 35/6]', '[305, 305, 1/3*w^3 + w^2 - 8/3*w - 35/3]', '[305, 305, -1/2*w^3 + 2*w^2 + 4*w - 37/2]', '[305, 305, 1/3*w^3 - 2*w^2 - 11/3*w + 61/3]', '[305, 305, 1/2*w^3 + w^2 - 3*w - 17/2]', '[311, 311, 2*w^2 - 13]', '[311, 311, -1/3*w^3 - 2*w^2 + 8/3*w + 50/3]', '[316, 158, 2/3*w^3 - 3*w^2 + 5/3*w + 14/3]', '[316, 158, -7/6*w^3 - 3*w^2 + 28/3*w + 113/6]', '[316, 158, -7/3*w^3 - 3*w^2 + 77/3*w + 116/3]', '[316, 158, 2/3*w^3 - 3*w^2 - 16/3*w + 77/3]', '[320, 20, 2*w + 2]', '[320, 20, -1/3*w^3 + 14/3*w - 7/3]', '[320, 40, w^3 + w^2 - 9*w - 9]', '[320, 40, 2/3*w^3 - w^2 - 13/3*w + 17/3]', '[324, 6, 1/2*w^3 - 7*w - 17/2]', '[324, 6, 3*w - 9]', '[324, 18, w^2 + w - 13]', '[324, 18, -w^2 - w + 4]', '[324, 18, 1/2*w^3 - w^2 - 4*w + 9/2]', '[324, 18, -w^2 - w + 2]', '[331, 331, 1/2*w^3 + w^2 - 4*w - 5/2]', '[331, 331, -1/2*w^3 - w^2 + 5*w + 27/2]', '[331, 331, 1/6*w^3 - 2*w^2 + 2/3*w + 73/6]', '[331, 331, 5/6*w^3 + 2*w^2 - 26/3*w - 103/6]', '[349, 349, -1/2*w^3 - w^2 + 4*w + 21/2]', '[349, 349, 1/6*w^3 + w^2 - 1/3*w - 59/6]', '[355, 355, -1/2*w^3 + 6*w + 11/2]', '[355, 355, -1/2*w^3 + 2*w^2 + 4*w - 27/2]', '[356, 178, 17/6*w^3 + 5*w^2 - 80/3*w - 271/6]', '[356, 178, -2/3*w^3 + w^2 + 31/3*w - 62/3]', '[356, 178, w^2 - 3*w - 2]', '[356, 178, -5/6*w^3 - 2*w^2 + 23/3*w + 97/6]', '[361, 19, 2/3*w^3 - 16/3*w - 7/3]', '[361, 19, 1/6*w^3 - 4/3*w - 29/6]', '[369, 123, -2/3*w^3 + 2*w^2 + 16/3*w - 41/3]', '[369, 123, w^3 - 10*w]', '[369, 123, -2/3*w^3 + 10/3*w + 1/3]', '[369, 123, -w^3 - 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2*w^2 + 2*w - 7/2]', '[1791, 597, -1/2*w^3 + w^2 + 5*w - 29/2]', '[1796, 898, w^3 - 7*w - 4]', '[1796, 898, -1/6*w^3 - 4*w^2 + 13/3*w + 113/6]', '[1796, 898, 7/6*w^3 - 31/3*w - 23/6]', '[1796, 898, -w^3 - 4*w^2 + 11*w + 40]', '[1801, 1801, -7/6*w^3 - w^2 + 28/3*w + 47/6]', '[1801, 1801, -w^3 + w^2 + 8*w - 7]', '[1804, 902, -2/3*w^3 - 2*w^2 + 25/3*w + 67/3]', '[1804, 902, 1/3*w^3 - w^2 - 11/3*w + 4/3]', '[1804, 902, 1/6*w^3 + 2*w^2 - 13/3*w - 41/6]', '[1804, 902, -1/3*w^3 - w^2 + 5/3*w + 41/3]', '[1804, 902, 1/3*w^3 + w^2 - 17/3*w - 2/3]', '[1804, 902, -1/6*w^3 - 2*w^2 + 1/3*w + 41/6]', '[1804, 902, -2*w^2 - w + 23]', '[1804, 902, -1/3*w^3 - w^2 + 17/3*w + 41/3]', '[1805, 95, 7/6*w^3 - 3*w^2 - 7/3*w + 31/6]', '[1805, 95, w^3 - 5*w^2 - 2*w + 19]', '[1811, 1811, 4/3*w^3 - 29/3*w - 26/3]', '[1811, 1811, -7/6*w^3 + w^2 + 31/3*w - 43/6]', '[1831, 1831, -1/3*w^3 + 2/3*w + 32/3]', '[1831, 1831, -3/2*w^3 - 2*w^2 + 12*w + 33/2]', '[1844, 922, 5/3*w^3 - 5*w^2 - 31/3*w + 95/3]', '[1844, 922, 2/3*w^3 - 4*w^2 - 7/3*w + 83/3]', '[1844, 922, -7/3*w^3 - 5*w^2 + 53/3*w + 92/3]', '[1844, 922, -31/6*w^3 - 8*w^2 + 157/3*w + 503/6]', '[1845, 615, -1/2*w^3 + 3*w^2 + 3*w - 41/2]', '[1845, 615, -w^3 + 4*w^2 + 8*w - 32]', '[1845, 615, 5/3*w^3 + 4*w^2 - 40/3*w - 82/3]', '[1845, 615, 7/6*w^3 + 3*w^2 - 31/3*w - 143/6]', '[1849, 43, -7/6*w^3 - 2*w^2 + 31/3*w + 125/6]', '[1849, 43, -1/2*w^3 + 3*w^2 + 5*w - 43/2]', '[1859, 143, -7/6*w^3 + 3*w^2 + 28/3*w - 121/6]', '[1859, 143, -5/6*w^3 - w^2 + 23/3*w + 19/6]', '[1859, 143, 5/6*w^3 + 3*w^2 - 11/3*w - 79/6]', '[1859, 143, -5/6*w^3 - w^2 + 26/3*w + 37/6]', '[1871, 1871, -3/2*w^3 - 2*w^2 + 12*w + 29/2]', '[1871, 1871, 7/6*w^3 - 2*w^2 - 28/3*w + 91/6]', '[1879, 1879, 3/2*w^3 + 3*w^2 - 13*w - 53/2]', '[1879, 1879, -5/6*w^3 + 3*w^2 + 17/3*w - 107/6]', '[1889, 1889, -1/2*w^3 - w^2 + 6*w + 5/2]', '[1889, 1889, w^2 - 2*w - 12]', '[1895, 1895, -7/6*w^3 + 31/3*w + 5/6]', '[1895, 1895, -1/2*w^3 + w^2 - 3/2]', '[1895, 1895, -13/6*w^3 + 10*w^2 + 10/3*w - 223/6]', '[1895, 1895, -w^3 + 7*w + 1]', '[1899, 633, -7/2*w^3 - 5*w^2 + 35*w + 115/2]', '[1899, 633, 7/2*w^3 + 7*w^2 - 36*w - 151/2]', '[1899, 633, -w^3 - w^2 + 10*w + 7]', '[1899, 633, -13/6*w^3 + 3*w^2 + 55/3*w - 97/6]', '[1901, 1901, w^2 + 2*w + 2]', '[1901, 1901, 1/2*w^3 - 3*w^2 + w + 13/2]', '[1901, 1901, -1/6*w^3 + 4*w^2 - 11/3*w - 73/6]', '[1901, 1901, 1/6*w^3 - w^2 - 10/3*w + 103/6]', '[1916, 958, w^3 - w^2 - 8*w + 6]', '[1916, 958, -7/6*w^3 - w^2 + 28/3*w + 53/6]', '[1916, 958, w^3 + 3*w^2 - 10*w - 28]', '[1916, 958, 1/6*w^3 - 3*w^2 + 2/3*w + 97/6]', '[1931, 1931, 7/6*w^3 - w^2 - 28/3*w + 13/6]', '[1931, 1931, 4/3*w^3 + w^2 - 32/3*w - 38/3]', '[1931, 1931, -7/6*w^3 - 3*w^2 + 31/3*w + 137/6]', '[1931, 1931, 1/2*w^3 - 3*w^2 - 3*w + 43/2]', '[1936, 22, w^3 - 8*w - 3]', '[1936, 22, -w^3 + 8*w + 1]', '[1936, 44, 1/3*w^3 + 3*w^2 - 11/3*w - 50/3]', '[1936, 44, -1/6*w^3 - 3*w^2 + 10/3*w + 95/6]', '[1936, 44, -2/3*w^3 - 3*w^2 + 22/3*w + 85/3]', '[1936, 44, 1/3*w^3 + 3*w^2 - 11/3*w - 83/3]', '[1936, 242, 1/3*w^3 - 20/3*w + 25/3]', '[1936, 242, 1/3*w^3 - 20/3*w - 23/3]', '[1936, 484, -1/2*w^3 + 3*w^2 - 2*w - 9/2]', '[1936, 484, 5/6*w^3 - 29/3*w - 1/6]', '[1936, 484, -1/3*w^3 - 1/3*w + 2/3]', '[1936, 484, -2*w^3 - 3*w^2 + 22*w + 39]', '[1945, 1945, -17/6*w^3 + 9*w^2 + 23/3*w - 185/6]', '[1945, 1945, 7/6*w^3 - 25/3*w + 7/6]', '[1949, 1949, 4/3*w^3 - 3*w^2 - 32/3*w + 58/3]', '[1949, 1949, 11/6*w^3 + 3*w^2 - 44/3*w - 151/6]', '[1951, 1951, 11/6*w^3 - 5*w^2 - 20/3*w + 113/6]', '[1951, 1951, -4/3*w^3 + 26/3*w - 1/3]', '[1964, 982, 4/3*w^3 - 5*w^2 - 11/3*w + 64/3]', '[1964, 982, -17/6*w^3 - 6*w^2 + 71/3*w + 253/6]', '[1964, 982, -10/3*w^3 - 5*w^2 + 101/3*w + 155/3]', '[1964, 982, 5/3*w^3 - 6*w^2 - 37/3*w + 140/3]', '[1975, 395, -5/6*w^3 + w^2 + 11/3*w - 29/6]', '[1975, 395, 3/2*w^3 + w^2 - 15*w - 19/2]', '[1980, 330, 3*w^2 - w - 14]', '[1980, 330, 4/3*w^3 - 4*w^2 - 23/3*w + 73/3]', '[1980, 330, 1/6*w^3 + 2*w^2 - 1/3*w - 53/6]', '[1980, 330, 5/2*w^3 + 4*w^2 - 23*w - 69/2]', '[1980, 330, -1/2*w^3 - w^2 + 6*w + 3/2]', '[1980, 330, 2/3*w^3 + 3*w^2 - 19/3*w - 91/3]', '[1980, 330, w^2 - 2*w - 13]', '[1980, 330, 2*w^2 + w - 21]', '[1991, 1991, 5/2*w^3 + 5*w^2 - 26*w - 105/2]', '[1991, 1991, 5/6*w^3 - 4*w^2 - 14/3*w + 167/6]', '[1991, 1991, -11/6*w^3 - 4*w^2 + 50/3*w + 187/6]', '[1991, 1991, -2/3*w^3 + 5*w^2 - 2/3*w - 62/3]', '[1996, 998, -2/3*w^3 + 25/3*w - 5/3]', '[1996, 998, -43/6*w^3 - 12*w^2 + 205/3*w + 683/6]', '[1996, 998, 2/3*w^3 + 3*w^2 - 25/3*w - 61/3]', '[1996, 998, -2*w^3 - 2*w^2 + 19*w + 25]', '[1999, 1999, -1/6*w^3 + 3*w^2 - 2/3*w - 151/6]', '[1999, 1999, 1/2*w^3 + 2*w^2 - 4*w - 49/2]', '[2000, 10, -w^3 + 2*w^2 + 2*w - 1]', '[2000, 20, 1/3*w^3 + w^2 - 17/3*w - 44/3]', '[2000, 20, 1/3*w^3 + w^2 - 17/3*w + 1/3]', '[2005, 2005, -3/2*w^3 + 9*w^2 - w - 63/2]', '[2005, 2005, 1/6*w^3 - 2*w^2 + 2/3*w + 97/6]', '[2005, 2005, 5/6*w^3 + 2*w^2 - 26/3*w - 79/6]', '[2005, 2005, 5/6*w^3 - 5*w^2 + 7/3*w + 89/6]', '[2011, 2011, -1/3*w^3 + 2*w^2 + 17/3*w - 37/3]', '[2011, 2011, 1/6*w^3 + 2*w^2 + 5/3*w - 107/6]', '[2020, 1010, -1/3*w^3 - 1/3*w + 8/3]', '[2020, 1010, -w^3 - 3*w^2 + 11*w + 28]', '[2020, 1010, -7/2*w^3 - 5*w^2 + 34*w + 101/2]', '[2020, 1010, -8/3*w^3 - 5*w^2 + 76/3*w + 133/3]', '[2025, 15, -w^3 + 8*w + 2]', '[2025, 45, -2/3*w^3 + 2*w^2 - 2/3*w - 5/3]', '[2025, 45, 2*w^3 + 2*w^2 - 22*w - 27]', '[2029, 2029, -11/3*w^3 - 6*w^2 + 100/3*w + 166/3]', '[2029, 2029, 5/6*w^3 - 2*w^2 - 38/3*w + 197/6]', '[2036, 1018, -w - 7]', '[2036, 1018, 2/3*w^3 + w^2 - 7/3*w - 19/3]', '[2036, 1018, -1/6*w^3 + 7/3*w - 43/6]', '[2036, 1018, -w^3 + w^2 + 11*w - 9]', '[2039, 2039, -11/6*w^3 - 3*w^2 + 47/3*w + 163/6]', '[2039, 2039, -1/6*w^3 + 3*w^2 + 1/3*w - 91/6]', '[2039, 2039, 7/6*w^3 - 3*w^2 - 25/3*w + 103/6]', '[2039, 2039, w^3 - 6*w^2 - 2*w + 26]', '[2045, 2045, -1/2*w^3 + 6*w^2 - 3*w - 49/2]', '[2045, 2045, 5/3*w^3 - 7*w^2 - 16/3*w + 95/3]', '[2061, 687, -7/6*w^3 + 3*w^2 + 40/3*w - 217/6]', '[2061, 687, 4/3*w^3 - 4*w^2 - 5/3*w + 28/3]', '[2061, 687, -4/3*w^3 + 2*w^2 + 26/3*w - 13/3]', '[2061, 687, 7/6*w^3 - 31/3*w - 17/6]', '[2061, 687, 3/2*w^3 + 2*w^2 - 12*w - 31/2]', '[2061, 687, w^3 - 7*w - 3]', '[2061, 687, -3/2*w^3 - w^2 + 17*w + 49/2]', '[2061, 687, -7/2*w^3 - 4*w^2 + 37*w + 97/2]', '[2084, 1042, 29/6*w^3 + 8*w^2 - 137/3*w - 445/6]', '[2084, 1042, -w^3 + w^2 + 16*w - 30]', '[2084, 1042, -2/3*w^3 + 3*w^2 + 13/3*w - 74/3]', '[2084, 1042, 7/6*w^3 + 2*w^2 - 19/3*w - 47/6]', '[2089, 2089, 3*w^2 - 4*w - 10]', '[2089, 2089, 2/3*w^3 - 5*w^2 + 8/3*w + 44/3]', '[2096, 262, 4*w - 14]', '[2096, 262, -7/3*w^3 - 4*w^2 + 56/3*w + 89/3]', '[2096, 524, 10/3*w^3 + 5*w^2 - 95/3*w - 149/3]', '[2096, 524, 1/2*w^3 - w^2 - 4*w + 29/2]', '[2096, 524, w^3 - 7*w - 2]', '[2096, 524, 1/3*w^3 - 23/3*w + 46/3]', '[2099, 2099, -7/6*w^3 - w^2 + 25/3*w + 77/6]', '[2099, 2099, 2*w^2 + w - 22]', '[2101, 2101, 19/6*w^3 + 6*w^2 - 100/3*w - 383/6]', '[2101, 2101, w^3 - 5*w^2 - 4*w + 31]', '[2101, 2101, 1/6*w^3 + 5/3*w - 23/6]', '[2101, 2101, -1/6*w^3 - w^2 + 1/3*w + 101/6]', '[2101, 2101, -3/2*w^3 - 2*w^2 + 11*w + 29/2]', '[2101, 2101, -7/6*w^3 - 3*w^2 + 37/3*w + 167/6]', '[2101, 2101, 8/3*w^3 + 6*w^2 - 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11/6]', '[881, 881, 4/3*w^3 + w^2 - 38/3*w - 38/3]', '[911, 911, 2*w^2 - 3*w - 4]', '[911, 911, -2/3*w^3 + 19/3*w - 20/3]', '[911, 911, 2/3*w^3 + w^2 - 22/3*w - 46/3]', '[911, 911, -2/3*w^3 + 4*w^2 - 2/3*w - 35/3]', '[919, 919, -1/6*w^3 + 3*w^2 - 11/3*w - 43/6]', '[919, 919, -13/6*w^3 - 4*w^2 + 55/3*w + 179/6]', '[919, 919, 5/6*w^3 - 2*w^2 - 8/3*w + 47/6]', '[919, 919, 4/3*w^3 - 4*w^2 - 29/3*w + 88/3]', '[929, 929, -7/6*w^3 + 3*w^2 + 10/3*w - 61/6]', '[929, 929, -1/2*w^3 + 2*w^2 + 4*w - 25/2]', '[929, 929, -2/3*w^3 + 22/3*w + 19/3]', '[929, 929, 2*w^2 - 4*w - 3]', '[961, 31, 5/6*w^3 - 20/3*w - 13/6]', '[961, 31, -5/6*w^3 + 20/3*w + 7/6]', '[971, 971, -7/6*w^3 + 6*w^2 + 4/3*w - 139/6]', '[971, 971, -2/3*w^3 + 2*w^2 + 1/3*w - 14/3]', '[991, 991, 7/3*w^3 + 4*w^2 - 59/3*w - 95/3]', '[991, 991, -1/6*w^3 + w^2 - 11/3*w + 47/6]', '[1009, 1009, -7/6*w^3 - w^2 + 31/3*w + 35/6]', '[1009, 1009, -5/6*w^3 + w^2 + 17/3*w - 53/6]', '[1021, 1021, -11/6*w^3 - 3*w^2 + 44/3*w + 139/6]', '[1021, 1021, 4/3*w^3 - 3*w^2 - 32/3*w + 64/3]', '[1021, 1021, -w^3 + 11*w + 3]', '[1021, 1021, 1/2*w^3 - w - 7/2]', '[1031, 1031, -w^3 + 6*w + 2]', '[1031, 1031, 4/3*w^3 - 38/3*w - 5/3]', '[1049, 1049, -w^3 + 4*w^2 + 3*w - 19]', '[1049, 1049, -5/2*w^3 - 4*w^2 + 25*w + 79/2]', '[1049, 1049, -2*w^3 - 4*w^2 + 18*w + 31]', '[1049, 1049, -w^3 + 4*w^2 + 6*w - 28]', '[1051, 1051, -3/2*w^3 - 2*w^2 + 13*w + 33/2]', '[1051, 1051, 1/6*w^3 - w^2 + 5/3*w - 17/6]', '[1061, 1061, 7/6*w^3 - 5*w^2 - 13/3*w + 157/6]', '[1061, 1061, -1/2*w^3 + 9*w + 23/2]', '[1091, 1091, -4/3*w^3 + 2*w^2 + 17/3*w - 16/3]', '[1091, 1091, -1/6*w^3 + 2*w^2 - 8/3*w - 13/6]', '[1109, 1109, -1/6*w^3 + 2*w^2 - 2/3*w - 91/6]', '[1109, 1109, -5/6*w^3 - 2*w^2 + 26/3*w + 85/6]', '[1151, 1151, -1/2*w^3 + 5*w - 13/2]', '[1151, 1151, -7/6*w^3 - w^2 + 31/3*w + 59/6]', '[1171, 1171, 5/6*w^3 - w^2 - 17/3*w + 23/6]', '[1171, 1171, 7/6*w^3 + w^2 - 31/3*w - 65/6]', '[1181, 1181, w^2 - 6*w + 10]', '[1181, 1181, -7/6*w^3 - w^2 + 46/3*w + 143/6]', '[1229, 1229, -5/3*w^3 - 3*w^2 + 46/3*w + 73/3]', '[1229, 1229, 1/6*w^3 - w^2 - 13/3*w + 109/6]', '[1229, 1229, 5/6*w^3 - 3*w^2 - 14/3*w + 119/6]', '[1229, 1229, -1/6*w^3 + w^2 + 13/3*w + 17/6]', '[1231, 1231, -2/3*w^3 + 25/3*w - 8/3]', '[1231, 1231, -1/6*w^3 - 5/3*w - 13/6]', '[1231, 1231, 1/2*w^3 - w - 3/2]', '[1231, 1231, w^3 - 11*w - 1]', '[1249, 1249, 1/3*w^3 + 3*w^2 - 14/3*w - 89/3]', '[1249, 1249, 7/6*w^3 - 2*w^2 - 25/3*w + 43/6]', '[1279, 1279, -17/6*w^3 - 5*w^2 + 80/3*w + 265/6]', '[1279, 1279, 4/3*w^3 - 5*w^2 - 20/3*w + 88/3]', '[1289, 1289, 5/6*w^3 + 2*w^2 - 23/3*w - 127/6]', '[1289, 1289, 1/2*w^3 + w^2 - 2*w - 21/2]', '[1291, 1291, -1/3*w^3 + 26/3*w - 46/3]', '[1291, 1291, -2/3*w^3 + 34/3*w + 43/3]', '[1301, 1301, 19/6*w^3 + 5*w^2 - 88/3*w - 275/6]', '[1301, 1301, -5/3*w^3 + 5*w^2 + 28/3*w - 83/3]', '[1321, 1321, -2*w^3 - 4*w^2 + 19*w + 34]', '[1321, 1321, -7/6*w^3 + 2*w^2 + 28/3*w - 97/6]', '[1321, 1321, 5/3*w^3 + 2*w^2 - 46/3*w - 64/3]', '[1321, 1321, 5/6*w^3 - 4*w^2 - 11/3*w + 149/6]', '[1381, 1381, -7/6*w^3 - 3*w^2 + 34/3*w + 167/6]', '[1381, 1381, 1/3*w^3 - 3*w^2 - 2/3*w + 49/3]', '[1399, 1399, 7/6*w^3 - 4*w^2 - 22/3*w + 163/6]', '[1399, 1399, 13/6*w^3 + 4*w^2 - 58/3*w - 191/6]', '[1409, 1409, -3/2*w^3 + 4*w^2 + 10*w - 45/2]', '[1409, 1409, 2*w^2 - 9]', '[1409, 1409, -5/2*w^3 - 4*w^2 + 22*w + 73/2]', '[1409, 1409, 1/3*w^3 + 2*w^2 - 8/3*w - 62/3]', '[1439, 1439, 7/6*w^3 - 37/3*w + 7/6]', '[1439, 1439, -1/2*w^3 - 3*w^2 + 7*w + 33/2]', '[1459, 1459, 2*w^2 - 2*w - 17]', '[1459, 1459, -5/6*w^3 + 26/3*w + 55/6]', '[1459, 1459, 2/3*w^3 + 2*w^2 - 22/3*w - 37/3]', '[1459, 1459, -1/2*w^3 + 2*w + 19/2]', '[1511, 1511, 3/2*w^3 - 6*w^2 - 8*w + 75/2]', '[1511, 1511, -19/6*w^3 - 6*w^2 + 88/3*w + 305/6]', '[1531, 1531, 5/2*w^3 + 3*w^2 - 29*w - 87/2]', '[1531, 1531, -13/6*w^3 - 3*w^2 + 61/3*w + 179/6]', '[1549, 1549, 1/2*w^3 + 2*w^2 - 6*w - 21/2]', '[1549, 1549, w^3 - 10*w + 2]', '[1579, 1579, -1/2*w^3 + w^2 + 3*w - 21/2]', '[1579, 1579, 5/6*w^3 + w^2 - 23/3*w - 25/6]', '[1601, 1601, 1/3*w^3 + w^2 - 20/3*w - 5/3]', '[1601, 1601, -7/6*w^3 - 3*w^2 + 31/3*w + 131/6]', '[1609, 1609, 5/6*w^3 - w^2 - 23/3*w + 23/6]', '[1609, 1609, -11/6*w^3 - 3*w^2 + 50/3*w + 175/6]', '[1609, 1609, -5/6*w^3 - w^2 + 17/3*w + 67/6]', '[1609, 1609, -w^3 + 3*w^2 + 6*w - 15]', '[1619, 1619, 1/3*w^3 + 2*w^2 - 5/3*w - 53/3]', '[1619, 1619, 2/3*w^3 - w^2 - 16/3*w + 2/3]', '[1619, 1619, 3/2*w^3 + 2*w^2 - 12*w - 39/2]', '[1619, 1619, 1/3*w^3 - 2*w^2 - 14/3*w + 70/3]', '[1621, 1621, 1/6*w^3 + 3*w^2 - 4/3*w - 113/6]', '[1621, 1621, -1/3*w^3 - 3*w^2 + 8/3*w + 77/3]', '[1681, 41, w^3 - 8*w - 4]', '[1699, 1699, 5/6*w^3 + w^2 - 29/3*w - 37/6]', '[1699, 1699, -1/6*w^3 + w^2 - 5/3*w - 49/6]', '[1709, 1709, -1/6*w^3 - 2*w^2 + 13/3*w + 35/6]', '[1709, 1709, -3/2*w^3 - w^2 + 14*w + 15/2]', '[1721, 1721, -5/6*w^3 - w^2 + 35/3*w + 103/6]', '[1721, 1721, 5/3*w^3 + 2*w^2 - 43/3*w - 61/3]', '[1721, 1721, -7/6*w^3 + 2*w^2 + 25/3*w - 55/6]', '[1721, 1721, -1/6*w^3 - w^2 + 19/3*w - 19/6]', '[1741, 1741, 1/6*w^3 - 3*w^2 + 5/3*w + 115/6]', '[1741, 1741, -1/2*w^3 + 4*w^2 - w - 25/2]', '[1741, 1741, 7/6*w^3 + 3*w^2 - 37/3*w - 149/6]', '[1741, 1741, -11/6*w^3 + 6*w^2 + 17/3*w - 131/6]', '[1789, 1789, 1/6*w^3 - w^2 - 13/3*w + 103/6]', '[1789, 1789, w^3 + 2*w^2 - 8*w - 18]', '[1789, 1789, -2*w^3 - 3*w^2 + 18*w + 30]', '[1789, 1789, -2/3*w^3 + 2*w^2 + 16/3*w - 35/3]', '[1801, 1801, -7/6*w^3 - w^2 + 28/3*w + 47/6]', '[1801, 1801, -w^3 + w^2 + 8*w - 7]', '[1811, 1811, 4/3*w^3 - 29/3*w - 26/3]', '[1811, 1811, -7/6*w^3 + w^2 + 31/3*w - 43/6]', '[1831, 1831, -1/3*w^3 + 2/3*w + 32/3]', '[1831, 1831, -3/2*w^3 - 2*w^2 + 12*w + 33/2]', '[1849, 43, -7/6*w^3 - 2*w^2 + 31/3*w + 125/6]', '[1849, 43, -1/2*w^3 + 3*w^2 + 5*w - 43/2]', '[1871, 1871, -3/2*w^3 - 2*w^2 + 12*w + 29/2]', '[1871, 1871, 7/6*w^3 - 2*w^2 - 28/3*w + 91/6]', '[1879, 1879, 3/2*w^3 + 3*w^2 - 13*w - 53/2]', '[1879, 1879, -5/6*w^3 + 3*w^2 + 17/3*w - 107/6]', '[1889, 1889, -1/2*w^3 - w^2 + 6*w + 5/2]', '[1889, 1889, w^2 - 2*w - 12]', '[1901, 1901, w^2 + 2*w + 2]', '[1901, 1901, 1/2*w^3 - 3*w^2 + w + 13/2]', '[1901, 1901, -1/6*w^3 + 4*w^2 - 11/3*w - 73/6]', '[1901, 1901, 1/6*w^3 - w^2 - 10/3*w + 103/6]', '[1931, 1931, 7/6*w^3 - w^2 - 28/3*w + 13/6]', '[1931, 1931, 4/3*w^3 + w^2 - 32/3*w - 38/3]', '[1931, 1931, -7/6*w^3 - 3*w^2 + 31/3*w + 137/6]', '[1931, 1931, 1/2*w^3 - 3*w^2 - 3*w + 43/2]', '[1949, 1949, 4/3*w^3 - 3*w^2 - 32/3*w + 58/3]', '[1949, 1949, 11/6*w^3 + 3*w^2 - 44/3*w - 151/6]', '[1951, 1951, 11/6*w^3 - 5*w^2 - 20/3*w + 113/6]', '[1951, 1951, -4/3*w^3 + 26/3*w - 1/3]', '[1999, 1999, -1/6*w^3 + 3*w^2 - 2/3*w - 151/6]', '[1999, 1999, 1/2*w^3 + 2*w^2 - 4*w - 49/2]']}

Column	Type
class_group	jsonb
class_number	numeric
cm	boolean
coeffs	numeric[]
conductor	numeric
degree	smallint
disc_abs	numeric
disc_rad	numeric
disc_sign	smallint
embeddings_gen_imag	double precision[]
embeddings_gen_real	double precision[]
gal_is_abelian	boolean
gal_is_cyclic	boolean
gal_is_solvable	boolean
galois_disc_exponents	numeric[]
galois_label	text
galt	integer
grd	double precision
index	integer
inessentialp	integer[]
is_galois	boolean
is_minimal_sibling	boolean
iso_number	smallint
label	text
local_algs	text[]
maximal_cm_subfield	numeric[]
minimal_sibling	numeric[]
monogenic	smallint
narrow_class_group	bigint[]
narrow_class_number	bigint
num_ram	smallint
r2	smallint
ramps	numeric[]
rd	double precision
regulator	numeric
relative_class_number	numeric
subfield_mults	integer[]
subfields	text[]
torsion_order	smallint
unit_signature_rank	smallint
used_grh	boolean

nf_fields • Show schema

{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [41, 9, -14, -1, 1], 'conductor': 0, 'degree': 4, 'disc_abs': 18625, 'disc_rad': 745, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 40.81507862588707, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.18625.1', 'local_algs': ['5.1.4.3a1.4', '149.2.1.0a1.1', '149.1.2.1a1.2'], 'monogenic': -1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [5, 149], 'rd': 11.6821847546, 'regulator': {'__RealLiteral__': 0, 'data': '8.81065543235', 'prec': 44}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_order': 2, 'unit_signature_rank': 3, 'used_grh': False}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.