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ec_curvedata • Show schema
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{'Ciso': '4851j', 'Clabel': '4851j2', 'Cnumber': 2, 'abc_quality': 1.0066941367119941, 'absD': 7565343767289, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 924, 'ainvs': [1, -1, 1, -5081, 45056], 'analytic_rank': 1, 'bad_primes': [3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4851, 'degree': 6912, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1630555614650502452992368092', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [169112377, 88209], 'lmfdb_iso': '4851.b', 'lmfdb_label': '4851.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -11, 0], 'min_quad_twist_disc': 21, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0.a.1', '28.12.0-2.a.1.1', '44.12.0.b.1', '84.24.0.?', '132.24.0.?', '308.24.0.?', '924.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 12, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5196058478563543570360960951', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.35920565739666125295106218098', 'prec': 107}, 'szpiro_ratio': 4.384761525460015, '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, 0, -1, -2, 0, 0, 3, 0, 2, -1, 0, 2, 0, 0, -1, -2, 0, 0, 2], 'aplist': [-1, 0, -2, 0, -1, 2, -2, 0, -8, 6, 8, 6, -2, 0, 8, -6, -4, -6, -4, 0, 14, -4, 12, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 4851, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '4851.b', 'trace_hash': 1738196544146408510}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.097674854963565061660390088104', 'prec': 107}, 'conductor': 4851, 'gens': [[6, 118, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5196058478563543570360960951', 'prec': 100}], 'lmfdb_label': '4851.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.65233108844474448215104361365', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9825722734782688426349378170623761706', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-75, 37, 1], [9, -5, 1]], 'xcoord_integral_points': [-75, -68, 6, 9, 72, 409, 1626]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [5, 0], '3': 'a', '5': [5, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4851.b2'}
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ec_torsion_growth • Show schema
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id: 253815
{'degree': 4, 'field': [-6, 30, -29, -2, 1], 'lmfdb_label': '4851.b2', 'torsion': [2, 4]}
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id: 253816
{'degree': 4, 'field': [22, 2, -1, -2, 1], 'lmfdb_label': '4851.b2', 'torsion': [2, 4]}
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id: 253814
{'degree': 4, 'field': [64, 0, -5, 0, 1], 'lmfdb_label': '4851.b2', 'torsion': [2, 4]}
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id: 253817
{'degree': 8, 'field': [-33, 140, -98, -3, 13, -7, 9, -1, 1], 'lmfdb_label': '4851.b2', 'torsion': [2, 6]}
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id: 253821
{'degree': 16, 'field': [2461, -14092, 34782, -56276, 71880, -72588, 63718, -47060, 30897, -17140, 8290, -3276, 1092, -280, 60, -8, 1], 'lmfdb_label': '4851.b2', 'torsion': [2, 8]}
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id: 253819
{'degree': 16, 'field': [3600, 0, -4548, 0, -1901, 0, 6188, 0, 3252, 0, 304, 0, 84, 0, 8, 0, 1], 'lmfdb_label': '4851.b2', 'torsion': [2, 8]}
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id: 253818
{'degree': 16, 'field': [71824, 0, -41752, 0, -799, 0, 5004, 0, -868, 0, -222, 0, 92, 0, 20, 0, 1], 'lmfdb_label': '4851.b2', 'torsion': [4, 4]}
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id: 253820
{'degree': 16, 'field': [43007364, 0, -70604568, 0, 18871584, 0, 720132, 0, 52597, 0, -26068, 0, 1614, 0, -64, 0, 1], 'lmfdb_label': '4851.b2', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 93688
{'conductor': 4851, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '4851.b2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 93689
{'conductor': 4851, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4851.b2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 93690
{'conductor': 4851, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4851.b2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1695648
{'adelic_gens': [[1, 0, 4, 1], [1, 4, 0, 1], [921, 4, 920, 5], [657, 658, 574, 265], [673, 532, 686, 141], [463, 266, 0, 1], [263, 0, 0, 923]], 'adelic_image': '924.48.0.?', 'conductor': 4851, 'lmfdb_label': '4851.b2', 'prime': 0}
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id: 24119
{'conductor': 4851, 'elladic_image': '2.6.0.1', 'lmfdb_label': '4851.b2', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 177250
{'lmfdb_iso': '4851.b', 'p': 5, 'prec': 20, 'unit': 1805069971496, 'val': 2}
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id: 177255
{'lmfdb_iso': '4851.b', 'p': 13, 'prec': 20, 'unit': 751474665009848357688, 'val': 1}
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id: 177257
{'lmfdb_iso': '4851.b', 'p': 17, 'prec': 20, 'unit': 203878115814039176798640, 'val': 1}
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id: 177253
{'lmfdb_iso': '4851.b', 'p': 23, 'prec': 20, 'unit': 67971828767325394499934732, 'val': 1}
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id: 177254
{'lmfdb_iso': '4851.b', 'p': 29, 'prec': 20, 'unit': 5993203610053722158735218291, 'val': 1}
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id: 177251
{'lmfdb_iso': '4851.b', 'p': 31, 'prec': 20, 'unit': 17415787949631618354219553541, 'val': 1}
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id: 177265
{'lmfdb_iso': '4851.b', 'p': 37, 'prec': 20, 'unit': 240958185292016523087592353655, 'val': 1}
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id: 177252
{'lmfdb_iso': '4851.b', 'p': 41, 'prec': 20, 'unit': 1726797532069073784705026224792, 'val': 1}
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id: 177263
{'lmfdb_iso': '4851.b', 'p': 47, 'prec': 20, 'unit': 48165116570593700112859310027679, 'val': 1}
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id: 177259
{'lmfdb_iso': '4851.b', 'p': 53, 'prec': 20, 'unit': 445128913060374264023915505353720, 'val': 1}
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id: 177260
{'lmfdb_iso': '4851.b', 'p': 59, 'prec': 20, 'unit': 650553324121412139802883702717289, 'val': 1}
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id: 177264
{'lmfdb_iso': '4851.b', 'p': 61, 'prec': 20, 'unit': 187195670601982295074204376061111, 'val': 1}
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id: 177249
{'lmfdb_iso': '4851.b', 'p': 67, 'prec': 20, 'unit': 21546471098308701144118866762779391, 'val': 1}
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id: 177261
{'lmfdb_iso': '4851.b', 'p': 73, 'prec': 20, 'unit': 98002170905128174089324438140917451, 'val': 1}
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id: 177256
{'lmfdb_iso': '4851.b', 'p': 79, 'prec': 20, 'unit': 814147429212741504443408787003838280, 'val': 1}
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id: 177258
{'lmfdb_iso': '4851.b', 'p': 83, 'prec': 20, 'unit': 1664448118232877941029406070003331226, 'val': 1}
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id: 177262
{'lmfdb_iso': '4851.b', 'p': 89, 'prec': 20, 'unit': 3478684405096766948989088849072705758, 'val': 1}
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id: 177248
{'lmfdb_iso': '4851.b', 'p': 97, 'prec': 20, 'unit': 14944756659068082913675835982935096283, 'val': 1}