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ec_curvedata • Show schema
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{'Ciso': '720a', 'Clabel': '720a1', 'Cnumber': 1, 'abc_quality': 1.292030029884618, 'absD': 138240, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 120, 'ainvs': [0, 0, 0, -3, 18], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 720, 'degree': 64, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.33358360290915185674185419390', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [-108, 5], 'lmfdb_iso': '720.a', 'lmfdb_label': '720.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -3, -18], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.d.1', '30.6.0.a.1', '40.6.0.e.1', '120.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.38183916910505176572288021703', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1858593255428003707716922710', 'prec': 103}, 'szpiro_ratio': 2.9340556290299626, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, -2, 0, 4, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, -1, -2, -2, 4, -2, -4, -8, -10, -4, 0, 0, 8, -8, 6, 14, -14, 4, -12, 6, 12, -4, -12, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 720, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '720.a', 'trace_hash': 675274654094818721}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.9487092022320144735253905953', 'prec': 100}, 'conductor': 720, 'gens': [[1, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.38183916910505176572288021703', 'prec': 103}], 'lmfdb_label': '720.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.7175526609099786316107569512', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0753361000821774599510267687185526672', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-3, 0, 1]], 'xcoord_integral_points': [-3, -2, 1, 3, 21]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '720.a2'}
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ec_torsion_growth • Show schema
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id: 33154
{'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '720.a2', 'torsion': [2, 2]}
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id: 33155
{'degree': 4, 'field': [-6, -12, -6, 0, 1], 'lmfdb_label': '720.a2', 'torsion': [4]}
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id: 33158
{'degree': 8, 'field': [-5, 16, -32, -2, 4, 4, -2, -2, 1], 'lmfdb_label': '720.a2', 'torsion': [6]}
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id: 33156
{'degree': 8, 'field': [1, 0, -2, 0, 18, 0, -2, 0, 1], 'lmfdb_label': '720.a2', 'torsion': [2, 4]}
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id: 33157
{'degree': 8, 'field': [16, 0, -17, 0, 9, 0, 7, 0, 1], 'lmfdb_label': '720.a2', 'torsion': [2, 4]}
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id: 33159
{'degree': 16, 'field': [-1472, 4608, -17152, 8448, 8000, -7296, 7232, 384, -2720, -2304, 1024, 480, -40, -48, -8, 0, 1], 'lmfdb_label': '720.a2', 'torsion': [8]}
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id: 33160
{'degree': 16, 'field': [15, -30, 54, -204, 342, -438, 612, -552, 472, -406, 214, -136, 82, -22, 16, -4, 1], 'lmfdb_label': '720.a2', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 8956
{'conductor': 720, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '720.a2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 8957
{'conductor': 720, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '720.a2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 8958
{'conductor': 720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '720.a2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1669206
{'adelic_gens': [[1, 2, 2, 5], [49, 76, 104, 15], [117, 4, 116, 5], [3, 4, 8, 11], [44, 1, 79, 0], [61, 4, 2, 9], [74, 1, 23, 0], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '120.12.0.?', 'conductor': 720, 'lmfdb_label': '720.a2', 'prime': 0}
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id: 3230
{'conductor': 720, 'elladic_image': '2.3.0.1', 'lmfdb_label': '720.a2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 13689
{'lmfdb_iso': '720.a', 'p': 7, 'prec': 20, 'unit': 1499267365949567, 'val': 2}
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id: 13688
{'lmfdb_iso': '720.a', 'p': 11, 'prec': 20, 'unit': 8488207278676552411, 'val': 1}
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id: 13693
{'lmfdb_iso': '720.a', 'p': 13, 'prec': 20, 'unit': 970453526356522090780, 'val': 1}
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id: 13695
{'lmfdb_iso': '720.a', 'p': 17, 'prec': 20, 'unit': 71753338141861306841253, 'val': 1}
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id: 13696
{'lmfdb_iso': '720.a', 'p': 19, 'prec': 20, 'unit': 1119784364011023826424312, 'val': 1}
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id: 13699
{'lmfdb_iso': '720.a', 'p': 23, 'prec': 20, 'unit': 10391490266410380698492265, 'val': 1}
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id: 13692
{'lmfdb_iso': '720.a', 'p': 29, 'prec': 20, 'unit': 4931619189954867555405180681, 'val': 1}
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id: 13705
{'lmfdb_iso': '720.a', 'p': 31, 'prec': 20, 'unit': 21174854261976677635765319453, 'val': 1}
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id: 13691
{'lmfdb_iso': '720.a', 'p': 43, 'prec': 20, 'unit': 9797335262412415939729831262118, 'val': 1}
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id: 13703
{'lmfdb_iso': '720.a', 'p': 47, 'prec': 20, 'unit': 4791530365903755908212936778261, 'val': 1}
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id: 13697
{'lmfdb_iso': '720.a', 'p': 53, 'prec': 20, 'unit': 417930614159498898807079438356345, 'val': 1}
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id: 13698
{'lmfdb_iso': '720.a', 'p': 59, 'prec': 20, 'unit': 2288659341263890354543647951823138, 'val': 1}
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id: 13704
{'lmfdb_iso': '720.a', 'p': 61, 'prec': 20, 'unit': 7531645154386492235995991056908444, 'val': 1}
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id: 13687
{'lmfdb_iso': '720.a', 'p': 67, 'prec': 20, 'unit': 529431346618083551045339923189751, 'val': 2}
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id: 13702
{'lmfdb_iso': '720.a', 'p': 71, 'prec': 20, 'unit': 143148844765935623027579484341805590, 'val': 1}
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id: 13690
{'lmfdb_iso': '720.a', 'p': 73, 'prec': 20, 'unit': 62352172160781087001507011230097721, 'val': 1}
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id: 13694
{'lmfdb_iso': '720.a', 'p': 79, 'prec': 20, 'unit': 555385397384411551122644650917864098, 'val': 1}
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id: 13700
{'lmfdb_iso': '720.a', 'p': 83, 'prec': 20, 'unit': 2357470829966919864495510384097272299, 'val': 1}
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id: 13701
{'lmfdb_iso': '720.a', 'p': 89, 'prec': 20, 'unit': 3614750223559974633205193647693580677, 'val': 1}
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id: 13686
{'lmfdb_iso': '720.a', 'p': 97, 'prec': 20, 'unit': 42052652490984335883023327172520061828, 'val': 1}