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ec_curvedata • Show schema
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{'Ciso': '51870m', 'Clabel': '51870m2', 'Cnumber': 2, 'abc_quality': 1.034318419400338, 'absD': 78687520727961600, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 103740, 'ainvs': [1, 1, 0, -4921287, 4200026229], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 51870, 'degree': 1769472, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4305838008545487283483627965', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2], 'jinv': [13181351126943641326385401, 78687520727961600], 'lmfdb_iso': '51870.l', 'lmfdb_label': '51870.l2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -4921287, 4200026229], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '60.12.0-2.a.1.1', '76.12.0.?', '364.12.0.?', '1140.24.0.?', '5460.24.0.?', '6916.24.0.?', '103740.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4305838008545487283483627965', 'prec': 100}, 'szpiro_ratio': 5.327763762438138, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -4, -1, -1, 1, -1, 1, 2, -1, -1, 1], 'aplist': [-1, -1, 1, -1, -4, -1, 2, -1, 0, 10, 8, 10, 6, -4, -8, 6, 0, -10, 12, -8, -6, -8, -12, 6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 51870, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '51870.l', 'trace_hash': 795013019310645010}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0077414396939366167013630234830', 'prec': 110}, 'conductor': 51870, 'gens': [], 'heights': [], 'lmfdb_label': '51870.l2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.30549330770657374144064877547', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2219732308262949657625951018851319225', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-2562, 1281, 1], [1278, -639, 1]], 'xcoord_integral_points': [-2562, 1278]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [4, 0], '3': [0, 0], '5': [1, 0], '7': [0, 0], '13': [0, 0], '19': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '51870.l2'}
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ec_torsion_growth • Show schema
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id: 2510592
{'degree': 4, 'field': [324, 0, -55, 0, 1], 'lmfdb_label': '51870.l2', 'torsion': [2, 4]}
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id: 2510591
{'degree': 4, 'field': [361, 0, 53, 0, 1], 'lmfdb_label': '51870.l2', 'torsion': [2, 4]}
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id: 2510590
{'degree': 4, 'field': [385, 20, -19, -2, 1], 'lmfdb_label': '51870.l2', 'torsion': [2, 4]}
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id: 2510593
{'degree': 8, 'field': [-768, 0, -113, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '51870.l2', 'torsion': [2, 6]}
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id: 2510594
{'degree': 16, 'field': [797497600, 0, -773289920, 0, 1871563136, 0, -351558588, 0, 27525089, 0, -1108164, 0, 23654, 0, -248, 0, 1], 'lmfdb_label': '51870.l2', 'torsion': [4, 4]}
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id: 2510595
{'degree': 16, 'field': [1215217159801225, 0, 43880436038400, 0, 1122290637130, 0, 32991515640, 0, 711332811, 0, 9695016, 0, 87286, 0, 456, 0, 1], 'lmfdb_label': '51870.l2', 'torsion': [2, 8]}
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id: 2510596
{'degree': 16, 'field': [2941311960150736, -1118337166366592, 1094164259134560, 48858333600320, -25662406843180, 1345472169504, -224902399688, -190769920640, 46593894645, 735601720, -150320948, 1732056, -277210, -5320, 780, -8, 1], 'lmfdb_label': '51870.l2', 'torsion': [2, 8]}
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id: 2510597
{'degree': 16, 'field': [474662643493522500, 0, -45471343148896500, 0, 938081935877625, 0, -11048232830040, 0, 70871129784, 0, -297090444, 0, 892780, 0, -1564, 0, 1], 'lmfdb_label': '51870.l2', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 1241065
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '51870.l2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1241066
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '51870.l2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1241067
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '51870.l2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 1241068
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '51870.l2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1241069
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '51870.l2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1241070
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '51870.l2', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 2008817
{'adelic_gens': [[1, 0, 4, 1], [41497, 4, 82994, 9], [103737, 4, 103736, 5], [51873, 4, 2, 3], [69161, 4, 34582, 9], [1, 4, 0, 1], [29641, 2, 0, 1], [47881, 2, 0, 1], [76443, 2, 87358, 103739]], 'adelic_image': '103740.48.0.?', 'conductor': 51870, 'lmfdb_label': '51870.l2', 'prime': 0}
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id: 222009
{'conductor': 51870, 'elladic_image': '2.6.0.1', 'lmfdb_label': '51870.l2', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 51870.l does not appear in ec_padic
