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ec_curvedata • Show schema
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{'Ciso': '4851g', 'Clabel': '4851g1', 'Cnumber': 1, 'abc_quality': 0.8976422655851721, 'absD': 101100503071953, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 132, 'ainvs': [1, -1, 0, 8811, 362074], 'analytic_rank': 1, 'bad_primes': [3, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 4851, 'degree': 18816, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3730616924084445644467806353', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 13, 'isogeny_degrees': [1], 'jinv': [17999471, 24057], 'lmfdb_iso': '4851.n', 'lmfdb_label': '4851.n1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 20, 41], 'min_quad_twist_disc': 21, 'modell_images': [], 'modm_images': ['132.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4286732453437655195898438689', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.47351788462915248465441047879', 'prec': 107}, 'szpiro_ratio': 4.6111417074142524, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 0, -1, -4, 0, 0, -3, 0, -4, 1, 0, 0, 0, 0, -1, 7, 0, -5, 4], 'aplist': [1, 0, -4, 0, 1, 0, 7, -5, 9, -1, 2, -3, 2, -1, -7, 0, -7, -10, -12, 15, -4, -8, -4, -12, -1], 'class_deg': 1, 'class_size': 1, 'conductor': 4851, 'isogeny_matrix': [[1]], 'lmfdb_iso': '4851.n', 'trace_hash': 879180584702118035}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.064176165904001906757467023432', 'prec': 107}, 'conductor': 4851, 'gens': [[86, 1280, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4286732453437655195898438689', 'prec': 100}], 'lmfdb_label': '4851.n1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.40285198148096458384694301662', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4532630866534571907977316780499303479', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [86]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 0], '7': 'a', '11': [2, 0], '13': [1, 1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4851.n1'}
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ec_torsion_growth • Show schema
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id: 253788
{'degree': 3, 'field': [-6, 12, -1, 1], 'lmfdb_label': '4851.n1', 'torsion': [2]}
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id: 253789
{'degree': 6, 'field': [2673, 0, 31, 0, -17, 0, 1], 'lmfdb_label': '4851.n1', 'torsion': [2, 2]}
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id: 253790
{'degree': 8, 'field': [-23, 89, -92, 5, 1, -7, 7, -4, 1], 'lmfdb_label': '4851.n1', 'torsion': [3]}
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id: 253791
{'degree': 12, 'field': [-132, 792, -429, -3960, 6599, -2100, 792, 476, -128, 44, 17, -4, 1], 'lmfdb_label': '4851.n1', 'torsion': [4]}
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ec_localdata • Show schema
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id: 93676
{'conductor': 4851, 'conductor_valuation': 2, 'discriminant_valuation': 13, 'j_denominator_valuation': 7, 'kodaira_symbol': -11, 'lmfdb_label': '4851.n1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 93677
{'conductor': 4851, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '4851.n1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
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id: 93678
{'conductor': 4851, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4851.n1', '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': [[89, 2, 89, 3], [1, 2, 0, 1], [67, 2, 67, 3], [1, 0, 2, 1], [131, 2, 130, 3], [13, 2, 13, 3], [1, 1, 131, 0]], 'adelic_image': '132.2.0.?', 'conductor': 4851, 'lmfdb_label': '4851.n1', 'prime': 0}
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ec_padic • Show schema
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id: 177193
{'lmfdb_iso': '4851.n', 'p': 5, 'prec': 20, 'unit': 10367785618259, 'val': -1}
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id: 177200
{'lmfdb_iso': '4851.n', 'p': 17, 'prec': 20, 'unit': 235530060433357251260071, 'val': 1}
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id: 177190
{'lmfdb_iso': '4851.n', 'p': 19, 'prec': 20, 'unit': 777497054672674834713009, 'val': 1}
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id: 177204
{'lmfdb_iso': '4851.n', 'p': 23, 'prec': 20, 'unit': 1481122246304444548712959, 'val': 1}
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id: 177198
{'lmfdb_iso': '4851.n', 'p': 29, 'prec': 20, 'unit': 1173656741476437455428064067, 'val': 1}
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id: 177195
{'lmfdb_iso': '4851.n', 'p': 31, 'prec': 20, 'unit': 16250666770264750528493678102, 'val': 1}
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id: 177208
{'lmfdb_iso': '4851.n', 'p': 37, 'prec': 20, 'unit': 54296741373199651067774886829, 'val': 1}
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id: 177196
{'lmfdb_iso': '4851.n', 'p': 41, 'prec': 20, 'unit': 3938256540524508372737134586862, 'val': 1}
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id: 177197
{'lmfdb_iso': '4851.n', 'p': 43, 'prec': 20, 'unit': 7042543000438272849959638092741, 'val': 1}
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id: 177206
{'lmfdb_iso': '4851.n', 'p': 47, 'prec': 20, 'unit': 21655551990698105185339674045688, 'val': 1}
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id: 177202
{'lmfdb_iso': '4851.n', 'p': 59, 'prec': 20, 'unit': 828348024935350137481068022671973, 'val': 1}
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id: 177207
{'lmfdb_iso': '4851.n', 'p': 61, 'prec': 20, 'unit': 5192281232264916914999568831495139, 'val': 1}
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id: 177192
{'lmfdb_iso': '4851.n', 'p': 67, 'prec': 20, 'unit': 21375570302164189704148292803899900, 'val': 1}
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id: 177194
{'lmfdb_iso': '4851.n', 'p': 71, 'prec': 20, 'unit': 104189381679257041536616774617288441, 'val': 1}
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id: 177203
{'lmfdb_iso': '4851.n', 'p': 73, 'prec': 20, 'unit': 177720219906542088175784405044706293, 'val': 1}
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id: 177199
{'lmfdb_iso': '4851.n', 'p': 79, 'prec': 20, 'unit': 656526059339008049820929071869290386, 'val': 1}
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id: 177201
{'lmfdb_iso': '4851.n', 'p': 83, 'prec': 20, 'unit': 1767700195462975415190147712712562923, 'val': 1}
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id: 177205
{'lmfdb_iso': '4851.n', 'p': 89, 'prec': 20, 'unit': 5025331608148316338962731277906164341, 'val': 1}
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id: 177191
{'lmfdb_iso': '4851.n', 'p': 97, 'prec': 20, 'unit': 34341610967407200503435119566661260611, 'val': 1}