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ec_curvedata • Show schema
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{'Ciso': '6240ba', 'Clabel': '6240ba2', 'Cnumber': 2, 'abc_quality': 0.9113907960857873, 'absD': 798720, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 1, 0, -1041, -13281], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6240, 'degree': 1536, 'elladic_images': ['8.12.0.12'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.31720244697946464121664093351', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2, 4], 'jinv': [30488290624, 195], 'lmfdb_iso': '6240.u', 'lmfdb_label': '6240.u1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1041, 13281], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.2', '52.12.0-4.c.1.1', '60.12.0-4.c.1.2', '104.24.0.?', '120.24.0.?', '780.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.4154642645684511207590650987', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37594473358048066820059118795', 'prec': 107}, 'szpiro_ratio': 3.714310250391046, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 2, 0, 4, 0], 'aplist': [0, 1, -1, 0, 0, -1, 2, 4, -4, -6, -8, -6, -2, -4, 0, 6, 0, -2, -8, 0, 6, 4, 12, 6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 6240, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '6240.u', 'trace_hash': 1522908264256824905}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.53025094998530603908333751521', 'prec': 103}, 'conductor': 6240, 'gens': [[149, 255, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '5.4154642645684511207590650987', 'prec': 100}], 'lmfdb_label': '6240.u1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.84043141678658218161992273900', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.5513263044283697000553108219321639564', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-19, 0, 1]], 'xcoord_integral_points': [-19]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '6240.u1'}
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ec_torsion_growth • Show schema
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id: 325283
{'degree': 2, 'field': [-195, 0, 1], 'lmfdb_label': '6240.u1', 'torsion': [2, 2]}
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id: 325285
{'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '6240.u1', 'torsion': [4]}
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id: 325284
{'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '6240.u1', 'torsion': [4]}
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id: 325286
{'degree': 4, 'field': [94, -34, 35, -2, 1], 'lmfdb_label': '6240.u1', 'torsion': [2, 4]}
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id: 325290
{'degree': 8, 'field': [-48, 0, 896, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '6240.u1', 'torsion': [6]}
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id: 325289
{'degree': 8, 'field': [19321, 0, 10412, 0, 1434, 0, 68, 0, 1], 'lmfdb_label': '6240.u1', 'torsion': [8]}
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id: 325287
{'degree': 8, 'field': [32061, 7908, -8244, 684, -371, 32, -6, -4, 1], 'lmfdb_label': '6240.u1', 'torsion': [2, 4]}
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id: 325288
{'degree': 8, 'field': [63001, 0, 11876, 0, 986, 0, 44, 0, 1], 'lmfdb_label': '6240.u1', 'torsion': [8]}
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id: 325294
{'degree': 16, 'field': [-20026295, 113550820, -222891216, 208030956, -121121418, 43204452, -9640444, 1420772, -413037, 239756, -73324, 7548, 594, -144, 12, -8, 1], 'lmfdb_label': '6240.u1', 'torsion': [2, 6]}
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id: 325293
{'degree': 16, 'field': [730486, -2875456, 5982444, -7699616, 7925574, -5949864, 3890068, -1927748, 870591, -293980, 95008, -21468, 5034, -700, 120, -8, 1], 'lmfdb_label': '6240.u1', 'torsion': [2, 8]}
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id: 325295
{'degree': 16, 'field': [921749, -335136, 3001498, -547016, 1315490, -241552, 49014, -28808, -35841, 928, -18, -232, 460, -44, 20, 0, 1], 'lmfdb_label': '6240.u1', 'torsion': [12]}
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id: 325292
{'degree': 16, 'field': [5642334, -6291504, 9436596, -7233864, 6163438, -3605280, 2194668, -1011892, 469079, -168124, 58784, -15148, 3738, -588, 104, -8, 1], 'lmfdb_label': '6240.u1', 'torsion': [2, 8]}
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id: 325296
{'degree': 16, 'field': [15595344, -12539520, 14478912, -3555840, 915720, 1182528, -623264, 160288, 8025, -37000, 12812, -3576, 1142, -280, 60, -8, 1], 'lmfdb_label': '6240.u1', 'torsion': [12]}
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id: 325291
{'degree': 16, 'field': [1027907721, 0, 591158232, 0, 33356130, 0, -4758348, 0, 320179, 0, 7588, 0, -450, 0, 28, 0, 1], 'lmfdb_label': '6240.u1', 'torsion': [4, 4]}
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ec_localdata • Show schema
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id: 124773
{'conductor': 6240, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '6240.u1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 124774
{'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6240.u1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 124775
{'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6240.u1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 124776
{'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6240.u1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1704890
{'adelic_gens': [[203, 198, 1370, 587], [848, 3, 725, 2], [628, 1, 1271, 6], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [524, 1, 1063, 6], [1553, 8, 1552, 9], [7, 6, 1554, 1555], [192, 967, 983, 996]], 'adelic_image': '1560.48.0.?', 'conductor': 6240, 'lmfdb_label': '6240.u1', 'prime': 0}
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id: 30649
{'conductor': 6240, 'elladic_image': '8.12.0.12', 'lmfdb_label': '6240.u1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 243721
{'lmfdb_iso': '6240.u', 'p': 17, 'prec': 20, 'unit': 133671140585920529623147, 'val': 1}
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id: 243713
{'lmfdb_iso': '6240.u', 'p': 19, 'prec': 20, 'unit': 593067524876225014776391, 'val': 1}
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id: 243725
{'lmfdb_iso': '6240.u', 'p': 23, 'prec': 20, 'unit': 36980586042475402933174660, 'val': 1}
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id: 243719
{'lmfdb_iso': '6240.u', 'p': 29, 'prec': 20, 'unit': 5968292521999215639417661201, 'val': 1}
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id: 243728
{'lmfdb_iso': '6240.u', 'p': 31, 'prec': 20, 'unit': 425219838713971828327877217, 'val': 2}
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id: 243716
{'lmfdb_iso': '6240.u', 'p': 37, 'prec': 20, 'unit': 341847618154736673357807780136, 'val': 1}
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id: 243717
{'lmfdb_iso': '6240.u', 'p': 41, 'prec': 20, 'unit': 29684500680985305461667602308, 'val': 2}
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id: 243718
{'lmfdb_iso': '6240.u', 'p': 43, 'prec': 20, 'unit': 7308063183007910668269488407892, 'val': 1}
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id: 243723
{'lmfdb_iso': '6240.u', 'p': 53, 'prec': 20, 'unit': 370944329369636622377605244257689, 'val': 1}
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id: 243727
{'lmfdb_iso': '6240.u', 'p': 61, 'prec': 20, 'unit': 5663243871933004621984000017254165, 'val': 1}
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id: 243715
{'lmfdb_iso': '6240.u', 'p': 67, 'prec': 20, 'unit': 33321117586371533873057782665771951, 'val': 1}
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id: 243724
{'lmfdb_iso': '6240.u', 'p': 73, 'prec': 20, 'unit': 201883703425417622863809799033056850, 'val': 1}
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id: 243720
{'lmfdb_iso': '6240.u', 'p': 79, 'prec': 20, 'unit': 84501877887643279330848479928849596, 'val': 1}
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id: 243722
{'lmfdb_iso': '6240.u', 'p': 83, 'prec': 20, 'unit': 596408807417395019230791792579669649, 'val': 1}
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id: 243726
{'lmfdb_iso': '6240.u', 'p': 89, 'prec': 20, 'unit': 6874182590046643732995667189045144422, 'val': 1}
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id: 243714
{'lmfdb_iso': '6240.u', 'p': 97, 'prec': 20, 'unit': 51123668236442257177167987120356653752, 'val': 1}