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ec_curvedata • Show schema
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{'Ciso': '78144be', 'Clabel': '78144be1', 'Cnumber': 1, 'abc_quality': 1.3018384230554119, 'absD': 32755555464192, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 444, 'ainvs': [0, 1, 0, -39253, 2967611], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 78144, 'degree': 184320, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4413457962341082670104738703', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 60, 'isogeny_degrees': [1, 2], 'jinv': [6532108386304000, 31987847133], 'lmfdb_iso': '78144.ci', 'lmfdb_label': '78144.ci2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -9813, 375858], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.b.1', '74.6.0.?', '444.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.0846965262359160088695959009', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.86372314576748717582944710242', 'prec': 103}, 'szpiro_ratio': 3.8474872002209874, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, -4, 0, -2, 0], 'aplist': [0, 1, 0, 0, -1, -2, -4, -2, 0, 4, -2, 1, 10, 2, -8, -10, 0, 10, 8, 16, 10, -14, -4, -4, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 78144, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '78144.ci', 'trace_hash': 2107152894911642264}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.055983874085888325194507246191', 'prec': 107}, 'conductor': 78144, 'gens': [[95, 324, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0846965262359160088695959009', 'prec': 100}], 'lmfdb_label': '78144.ci2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.66003128052056816576232444459', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.1593363718770370637808656632863061094', 'prec': 130}, 'tamagawa_product': 40, 'torsion_generators': [[-229, 0, 1]], 'xcoord_integral_points': [-229, 95, 134]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [2, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '78144.ci2'}
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ec_torsion_growth • Show schema
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id: 3688648
{'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '78144.ci2', 'torsion': [2, 2]}
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id: 3688649
{'degree': 4, 'field': [37, 0, 16, 0, 1], 'lmfdb_label': '78144.ci2', 'torsion': [4]}
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id: 3688652
{'degree': 8, 'field': [-768, 0, 12512, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '78144.ci2', 'torsion': [6]}
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id: 3688650
{'degree': 8, 'field': [9, 0, 84, 0, 91, 0, 28, 0, 1], 'lmfdb_label': '78144.ci2', 'torsion': [2, 4]}
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id: 3688651
{'degree': 8, 'field': [441, 0, -848, 0, 170, 0, -16, 0, 1], 'lmfdb_label': '78144.ci2', 'torsion': [2, 4]}
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id: 3688654
{'degree': 16, 'field': [12894715233, 493822728, -584660172, 219043776, -199162086, 96998216, -14772880, -14944072, 3616259, 58184, 9008, -9992, 634, 448, -44, -8, 1], 'lmfdb_label': '78144.ci2', 'torsion': [2, 6]}
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id: 3688653
{'degree': 16, 'field': [23260520196, 0, 26639381952, 0, 7772084136, 0, 93701760, 0, 1794784, 0, 354704, 0, 8748, 0, 128, 0, 1], 'lmfdb_label': '78144.ci2', 'torsion': [8]}
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ec_localdata • Show schema
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id: 1901476
{'conductor': 78144, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '78144.ci2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 1901477
{'conductor': 78144, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '78144.ci2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
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id: 1901478
{'conductor': 78144, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '78144.ci2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1901479
{'conductor': 78144, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '78144.ci2', 'prime': 37, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2179921
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [337, 112, 332, 111], [149, 4, 298, 9], [441, 4, 440, 5], [374, 1, 35, 0]], 'adelic_image': '444.12.0.?', 'conductor': 78144, 'lmfdb_label': '78144.ci2', 'prime': 0}
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id: 322099
{'conductor': 78144, 'elladic_image': '2.3.0.1', 'lmfdb_label': '78144.ci2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 4023249
{'lmfdb_iso': '78144.ci', 'p': 13, 'prec': 20, 'unit': 1173076602039541586515, 'val': 1}
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id: 4023251
{'lmfdb_iso': '78144.ci', 'p': 17, 'prec': 20, 'unit': 7025459636377073148195, 'val': 1}
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id: 4023252
{'lmfdb_iso': '78144.ci', 'p': 19, 'prec': 20, 'unit': 1641387337568503230464014, 'val': 1}
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id: 4023248
{'lmfdb_iso': '78144.ci', 'p': 29, 'prec': 20, 'unit': 6042273056727273208008970984, 'val': 1}
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id: 4023258
{'lmfdb_iso': '78144.ci', 'p': 31, 'prec': 20, 'unit': 322054490110457008815759499, 'val': 1}
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id: 4023246
{'lmfdb_iso': '78144.ci', 'p': 41, 'prec': 20, 'unit': 662043942263017235906015102826, 'val': 1}
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id: 4023247
{'lmfdb_iso': '78144.ci', 'p': 43, 'prec': 20, 'unit': 3072774085492901425773267733461, 'val': 1}
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id: 4023250
{'lmfdb_iso': '78144.ci', 'p': 47, 'prec': 20, 'unit': 55693331051407553562828176923338, 'val': 1}
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id: 4023253
{'lmfdb_iso': '78144.ci', 'p': 53, 'prec': 20, 'unit': 142887756496696451021008862982287, 'val': 1}
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id: 4023257
{'lmfdb_iso': '78144.ci', 'p': 61, 'prec': 20, 'unit': 8118908214484033792512827061937680, 'val': 1}
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id: 4023244
{'lmfdb_iso': '78144.ci', 'p': 67, 'prec': 20, 'unit': 9475687141517557342344548536257605, 'val': 1}
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id: 4023245
{'lmfdb_iso': '78144.ci', 'p': 71, 'prec': 20, 'unit': 27115026643960435618801378904406711, 'val': 1}
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id: 4023254
{'lmfdb_iso': '78144.ci', 'p': 73, 'prec': 20, 'unit': 172796728210868132049873810385202908, 'val': 1}
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id: 4023256
{'lmfdb_iso': '78144.ci', 'p': 79, 'prec': 20, 'unit': 168735973000824991772477573979717328, 'val': 1}
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id: 4023243
{'lmfdb_iso': '78144.ci', 'p': 83, 'prec': 20, 'unit': 2095551578336938477544126675026237873, 'val': 1}
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id: 4023255
{'lmfdb_iso': '78144.ci', 'p': 89, 'prec': 20, 'unit': 3264545309748492393663471640498678127, 'val': 1}
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id: 4023242
{'lmfdb_iso': '78144.ci', 'p': 97, 'prec': 20, 'unit': 157422850159022541560794218403229852, 'val': 1}