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ec_curvedata • Show schema
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{'Ciso': '72324f', 'Clabel': '72324f1', 'Cnumber': 1, 'abc_quality': 0.6865353188138825, 'absD': 44109859094784, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 492, 'ainvs': [0, 0, 0, -19551, -1099658], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 41], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 72324, 'degree': 241920, 'elladic_images': ['3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3770688340944117242345207519', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 20, 'isogeny_degrees': [1, 3], 'jinv': [-768208, 41], 'lmfdb_iso': '72324.u', 'lmfdb_label': '72324.u1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -44, -104], 'min_quad_twist_disc': 21, 'modell_images': ['3B.1.2'], 'modm_images': ['3.8.0-3.a.1.1', '164.2.0.?', '492.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.93160886331648219781149177650', 'prec': 107}, 'szpiro_ratio': 3.6951016928869698, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, -4, 0, 0, 0, 0, 0, -7, 0], 'aplist': [0, 0, 3, 0, -3, -4, 0, -7, -6, -6, -10, 2, 1, -4, -12, 6, -6, -13, -4, 9, 14, -1, -12, 12, 2], 'class_deg': 3, 'class_size': 2, 'conductor': 72324, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '72324.u', 'trace_hash': 710193510308044435}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.063663895407056790472158242274', 'prec': 107}, 'conductor': 72324, 'gens': [], 'heights': [], 'lmfdb_label': '72324.u1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20124788503985157240404115196', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.60374365511955471721212345586617225798', 'prec': 133}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': 'a', '11': [0, 0], '13': [0, 0], '17': [0, 0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [1, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '72324.u1'}
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ec_torsion_growth • Show schema
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id: 3428913
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '72324.u1', 'torsion': [3]}
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id: 3428914
{'degree': 3, 'field': [-28, 14, 0, 1], 'lmfdb_label': '72324.u1', 'torsion': [2]}
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id: 3428915
{'degree': 3, 'field': [1233, -191, -1, 1], 'lmfdb_label': '72324.u1', 'torsion': [3]}
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id: 3428916
{'degree': 6, 'field': [41, 0, -1, 0, 23, 0, 1], 'lmfdb_label': '72324.u1', 'torsion': [2, 2]}
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id: 3428918
{'degree': 6, 'field': [784, 392, 196, -56, -14, 0, 1], 'lmfdb_label': '72324.u1', 'torsion': [6]}
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id: 3428917
{'degree': 6, 'field': [2392347, 0, -5357, 0, 1, 0, 1], 'lmfdb_label': '72324.u1', 'torsion': [3, 3]}
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id: 3428919
{'degree': 9, 'field': [-8, 128, -300, 354, -128, 150, -6, 32, 0, 1], 'lmfdb_label': '72324.u1', 'torsion': [6]}
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id: 3428920
{'degree': 12, 'field': [-3851, 8558, -6520, -454, 3629, -1960, 0, 392, -167, 22, 12, -6, 1], 'lmfdb_label': '72324.u1', 'torsion': [4]}
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id: 3428921
{'degree': 12, 'field': [1681, 0, 41, 0, -942, 0, 105, 0, 530, 0, -23, 0, 1], 'lmfdb_label': '72324.u1', 'torsion': [2, 6]}
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id: 3428922
{'degree': 18, 'field': [1, 9, 54, 223, 699, 1281, 2319, 3036, 4749, 4605, 4020, 1812, 722, -39, 12, -22, 9, 0, 1], 'lmfdb_label': '72324.u1', 'torsion': [9]}
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id: 3428924
{'degree': 18, 'field': [64, 576, 4128, 15936, 36384, -912, -40156, -77712, 150612, 292048, 205044, 56484, -4252, -3264, 258, -12, -18, 0, 1], 'lmfdb_label': '72324.u1', 'torsion': [2, 6]}
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id: 3428923
{'degree': 18, 'field': [64, 1024, 13984, 32736, 43664, 74632, 67812, -43664, -30324, 24536, 10276, -6992, -4056, 320, 874, -12, -32, 0, 1], 'lmfdb_label': '72324.u1', 'torsion': [3, 6]}
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ec_localdata • Show schema
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id: 1753698
{'conductor': 72324, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '72324.u1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 1753699
{'conductor': 72324, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '72324.u1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 1753700
{'conductor': 72324, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '72324.u1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
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id: 1753701
{'conductor': 72324, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '72324.u1', 'prime': 41, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2142085
{'adelic_gens': [[247, 6, 249, 19], [4, 3, 9, 7], [489, 490, 482, 485], [457, 6, 387, 19], [487, 6, 486, 7], [450, 35, 287, 81], [1, 6, 0, 1], [3, 4, 8, 11], [1, 0, 6, 1]], 'adelic_image': '492.16.0.?', 'conductor': 72324, 'lmfdb_label': '72324.u1', 'prime': 0}
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id: 300331
{'conductor': 72324, 'elladic_image': '3.8.0.2', 'lmfdb_label': '72324.u1', 'modell_image': '3B.1.2', 'prime': 3}
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lmfdb_iso 72324.u does not appear in ec_padic