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ec_curvedata • Show schema
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{'Ciso': '4400h', 'Clabel': '4400h1', 'Cnumber': 1, 'abc_quality': 0.7710622198826756, 'absD': 44000000000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 440, 'ainvs': [0, 1, 0, 792, 5588], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 4400, 'degree': 1920, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.73017016460730852464338906769', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 20, 'isogeny_degrees': [1], 'jinv': [13718, 11], 'lmfdb_iso': '4400.u', 'lmfdb_label': '4400.u1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 32, -32], 'min_quad_twist_disc': -20, 'modell_images': [], 'modm_images': ['440.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.70842057205772260609994954169', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 55], [5, 14, 176], [11, 12, 400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1122931852315499566063098769', 'prec': 103}, 'szpiro_ratio': 3.770970013833393, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 0, 0, -1, 0, -2, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0], 'aplist': [0, 1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 1, 0, -6, -8, 9, -4, -7, 4, -5, 14, -4, -16, -7, -16], 'class_deg': 1, 'class_size': 1, 'conductor': 4400, 'isogeny_matrix': [[1]], 'lmfdb_iso': '4400.u', 'trace_hash': 238272003255306666}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.23215725138851301729292412871', 'prec': 103}, 'conductor': 4400, 'gens': [[58, 500, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.70842057205772260609994954169', 'prec': 103}], 'lmfdb_label': '4400.u1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.73414134670313314373491782741', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1606466624212835812342411858175191636', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [4, 58]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [3, 0], '5': 'a', '7': [1, 0], '11': [4, 0], '13': [1, 1, 0], '17': [3, 0], '19': [1, 0], '23': [3, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4400.u1'}
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ec_torsion_growth • Show schema
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id: 228705
{'degree': 3, 'field': [-8, 2, 0, 1], 'lmfdb_label': '4400.u1', 'torsion': [2]}
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id: 228706
{'degree': 6, 'field': [16, -32, 118, 16, -7, -2, 1], 'lmfdb_label': '4400.u1', 'torsion': [2, 2]}
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id: 228707
{'degree': 8, 'field': [366, -724, 74, 192, -96, -6, 6, -2, 1], 'lmfdb_label': '4400.u1', 'torsion': [3]}
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id: 228708
{'degree': 12, 'field': [-7039, 19527, -13420, -32417, -24257, -12118, -1520, 1450, 527, -41, -36, -1, 1], 'lmfdb_label': '4400.u1', 'torsion': [4]}
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ec_localdata • Show schema
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id: 83163
{'conductor': 4400, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '4400.u1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 83164
{'conductor': 4400, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4400.u1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 83165
{'conductor': 4400, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4400.u1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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{'adelic_gens': [[439, 2, 438, 3], [221, 2, 221, 3], [321, 2, 321, 3], [1, 1, 439, 0], [1, 0, 2, 1], [1, 2, 0, 1], [111, 2, 0, 1], [177, 2, 177, 3]], 'adelic_image': '440.2.0.?', 'conductor': 4400, 'lmfdb_label': '4400.u1', 'prime': 0}
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ec_padic • Show schema
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id: 156435
{'lmfdb_iso': '4400.u', 'p': 7, 'prec': 20, 'unit': 9222405185601738, 'val': 1}
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id: 156440
{'lmfdb_iso': '4400.u', 'p': 17, 'prec': 20, 'unit': 2230564314174298509035300, 'val': 0}
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id: 156431
{'lmfdb_iso': '4400.u', 'p': 19, 'prec': 20, 'unit': 1516680283240845577214890, 'val': 1}
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id: 156438
{'lmfdb_iso': '4400.u', 'p': 29, 'prec': 20, 'unit': 4413151346193248148970558132, 'val': 1}
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id: 156448
{'lmfdb_iso': '4400.u', 'p': 31, 'prec': 20, 'unit': 215368623487601635231180272781, 'val': -1}
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id: 156434
{'lmfdb_iso': '4400.u', 'p': 37, 'prec': 20, 'unit': 1384457394972937891276318445185, 'val': -1}
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id: 156437
{'lmfdb_iso': '4400.u', 'p': 43, 'prec': 20, 'unit': 9900394859532308862515051587968, 'val': 1}
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id: 156446
{'lmfdb_iso': '4400.u', 'p': 47, 'prec': 20, 'unit': 39467220929839869578622829952691, 'val': 1}
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id: 156442
{'lmfdb_iso': '4400.u', 'p': 53, 'prec': 20, 'unit': 303433130986057898119852324484890, 'val': 1}
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id: 156443
{'lmfdb_iso': '4400.u', 'p': 59, 'prec': 20, 'unit': 1415121295840992529079023328270485, 'val': 1}
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id: 156447
{'lmfdb_iso': '4400.u', 'p': 61, 'prec': 20, 'unit': 4226712529049178933174887945151576, 'val': 1}
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id: 156433
{'lmfdb_iso': '4400.u', 'p': 67, 'prec': 20, 'unit': 11050805605001453292512485679443957, 'val': 1}
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id: 156445
{'lmfdb_iso': '4400.u', 'p': 71, 'prec': 20, 'unit': 121910693757323074640536124587847240, 'val': 1}
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id: 156436
{'lmfdb_iso': '4400.u', 'p': 73, 'prec': 20, 'unit': 67076640334839089772956848178892532, 'val': 1}
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id: 156439
{'lmfdb_iso': '4400.u', 'p': 79, 'prec': 20, 'unit': 195969097663301235061279930564182371, 'val': 1}
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id: 156441
{'lmfdb_iso': '4400.u', 'p': 83, 'prec': 20, 'unit': 1581524211403656309480981534982665213, 'val': 1}
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id: 156444
{'lmfdb_iso': '4400.u', 'p': 89, 'prec': 20, 'unit': 3549372511953892615996284396546131459, 'val': 1}
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id: 156432
{'lmfdb_iso': '4400.u', 'p': 97, 'prec': 20, 'unit': 49974459215200201432338729207784124077, 'val': 1}