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ec_curvedata • Show schema
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{'Ciso': '1248i', 'Clabel': '1248i2', 'Cnumber': 2, 'abc_quality': 0.8900787468395513, 'absD': 6230016, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 1, 0, 31, 111], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1248, 'degree': 256, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.011724719246324406964900843237', 'prec': 110}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2], 'jinv': [778688, 1521], 'lmfdb_iso': '1248.g', 'lmfdb_label': '1248.g2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 31, -111], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '24.12.0-4.a.1.1', '52.12.0.d.1', '104.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.85228445168330335711247697213', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.70487189980626971638213296470', 'prec': 107}, 'szpiro_ratio': 3.1908117129429825, '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, -2, 0, 2, 0, 1, 0, -6, 0, -1, 0, -2, 0, -2, 0, -6, 0], 'aplist': [0, 1, -2, 2, -6, -1, -2, -6, 0, -6, 6, 2, -10, 8, 6, 6, -6, -10, 2, -14, -14, 4, 6, 6, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 1248, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1248.g', 'trace_hash': 1256218849839652146}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.0237265382811552258731387085', 'prec': 100}, 'conductor': 1248, 'gens': [[1, 12, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.85228445168330335711247697213', 'prec': 103}], 'lmfdb_label': '1248.g2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.6449373911122734516236278001', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8039091248749749993315493375085687268', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-3, 0, 1]], 'xcoord_integral_points': [-3, 1, 10]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [6, 0], '5': [3, 0], '7': [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': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1248.g2'}
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ec_torsion_growth • Show schema
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id: 62112
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1248.g2', 'torsion': [2, 2]}
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id: 62113
{'degree': 4, 'field': [-1, 0, -3, 0, 1], 'lmfdb_label': '1248.g2', 'torsion': [4]}
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id: 62116
{'degree': 8, 'field': [-243, 0, -144, 0, 54, 0, 0, 0, 1], 'lmfdb_label': '1248.g2', 'torsion': [6]}
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id: 62115
{'degree': 8, 'field': [9, -6, 2, -10, 7, -6, 8, -4, 1], 'lmfdb_label': '1248.g2', 'torsion': [2, 4]}
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id: 62114
{'degree': 8, 'field': [25, 20, -54, -28, 80, -32, -2, 0, 1], 'lmfdb_label': '1248.g2', 'torsion': [2, 4]}
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id: 62117
{'degree': 16, 'field': [529, -3772, 9378, -7472, -3750, 4500, 3958, -1244, -2697, 128, 1642, -660, -72, 56, 12, -8, 1], 'lmfdb_label': '1248.g2', 'torsion': [4, 4]}
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id: 62119
{'degree': 16, 'field': [5972, -28064, 47584, -40464, 21160, -3256, 2896, -4208, 2700, -992, 320, -256, 176, -84, 32, -8, 1], 'lmfdb_label': '1248.g2', 'torsion': [2, 6]}
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id: 62118
{'degree': 16, 'field': [120409, 0, 110212, 0, 34830, 0, -5752, 0, -6017, 0, -1168, 0, -30, 0, 28, 0, 1], 'lmfdb_label': '1248.g2', 'torsion': [8]}
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ec_localdata • Show schema
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id: 18542
{'conductor': 1248, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '1248.g2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 18543
{'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1248.g2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 18544
{'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1248.g2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1672427
{'adelic_gens': [[209, 8, 106, 17], [3, 8, 10, 27], [1, 0, 8, 1], [235, 4, 273, 1], [1, 8, 0, 1], [157, 4, 2, 9], [5, 8, 48, 77], [305, 8, 304, 9], [145, 2, 0, 1]], 'adelic_image': '312.48.0.?', 'conductor': 1248, 'lmfdb_label': '1248.g2', 'prime': 0}
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id: 5986
{'conductor': 1248, 'elladic_image': '4.6.0.5', 'lmfdb_label': '1248.g2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 31227
{'lmfdb_iso': '1248.g', 'p': 5, 'prec': 20, 'unit': 476581290056, 'val': 3}
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id: 31228
{'lmfdb_iso': '1248.g', 'p': 7, 'prec': 20, 'unit': 784837897883660, 'val': 1}
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id: 31234
{'lmfdb_iso': '1248.g', 'p': 11, 'prec': 20, 'unit': 46553682261896740086, 'val': 1}
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id: 31235
{'lmfdb_iso': '1248.g', 'p': 17, 'prec': 20, 'unit': 90081814833338397353261, 'val': 1}
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id: 31236
{'lmfdb_iso': '1248.g', 'p': 19, 'prec': 20, 'unit': 1427557374173504200059673, 'val': 1}
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id: 31232
{'lmfdb_iso': '1248.g', 'p': 29, 'prec': 20, 'unit': 3527498697899453437067638323, 'val': 1}
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id: 31229
{'lmfdb_iso': '1248.g', 'p': 31, 'prec': 20, 'unit': 5539508691514205157731698528, 'val': 1}
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id: 31244
{'lmfdb_iso': '1248.g', 'p': 37, 'prec': 20, 'unit': 351171046314358733858135822344, 'val': 1}
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id: 31230
{'lmfdb_iso': '1248.g', 'p': 41, 'prec': 20, 'unit': 691796841992755289695522435483, 'val': 1}
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id: 31231
{'lmfdb_iso': '1248.g', 'p': 43, 'prec': 20, 'unit': 6392574191733778650133364170679, 'val': 1}
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id: 31242
{'lmfdb_iso': '1248.g', 'p': 47, 'prec': 20, 'unit': 49628016275846055254397972534656, 'val': 1}
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id: 31237
{'lmfdb_iso': '1248.g', 'p': 53, 'prec': 20, 'unit': 365784654721064157579890594557097, 'val': 1}
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id: 31238
{'lmfdb_iso': '1248.g', 'p': 59, 'prec': 20, 'unit': 795282375596032609932732490311302, 'val': 1}
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id: 31243
{'lmfdb_iso': '1248.g', 'p': 61, 'prec': 20, 'unit': 6131691982826156013676926753827983, 'val': 1}
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id: 31226
{'lmfdb_iso': '1248.g', 'p': 67, 'prec': 20, 'unit': 8565565935472346896280662321916976, 'val': 1}
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id: 31241
{'lmfdb_iso': '1248.g', 'p': 71, 'prec': 20, 'unit': 70325198262372167721894301602897328, 'val': 1}
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id: 31239
{'lmfdb_iso': '1248.g', 'p': 73, 'prec': 20, 'unit': 22692539589005904841924737472680429, 'val': 1}
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id: 31233
{'lmfdb_iso': '1248.g', 'p': 79, 'prec': 20, 'unit': 757722650766473802953549875720567484, 'val': 1}
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id: 31225
{'lmfdb_iso': '1248.g', 'p': 83, 'prec': 20, 'unit': 521769139542171560497342230500890492, 'val': 1}
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id: 31240
{'lmfdb_iso': '1248.g', 'p': 89, 'prec': 20, 'unit': 3872074955948847401208346121858295295, 'val': 1}
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id: 31224
{'lmfdb_iso': '1248.g', 'p': 97, 'prec': 20, 'unit': 21939060648481621769983931770674152835, 'val': 1}