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ec_curvedata • Show schema
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{'Ciso': '7007c', 'Clabel': '7007c1', 'Cnumber': 1, 'abc_quality': 1.057759724031501, 'absD': 2037716327647, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 616, 'ainvs': [1, -1, 1, -769, 69360], 'analytic_rank': 0, 'bad_primes': [7, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 7007, 'degree': 7296, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0420358121509936525755781536', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [-426957777, 17320303], 'lmfdb_iso': '7007.b', 'lmfdb_label': '7007.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -16, -198], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '14.6.0.b.1', '28.24.0-28.g.1.2', '88.24.0.?', '616.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.069080737623337000022901781879', 'prec': 107}, 'szpiro_ratio': 4.04439193937996, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, -1, 2, 0, 0, 3, -3, -2, 1, 0, 1, 0, 0, -1, 2, 3, 4, -2], 'aplist': [-1, 0, 2, 0, 1, 1, 2, 4, 0, 6, 4, 6, -6, 12, -4, -10, 0, -10, 12, 0, -14, 0, 4, 14, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 7007, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '7007.b', 'trace_hash': 1940209168086223941}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.12442257746081212624783175092', 'prec': 103}, 'conductor': 7007, 'gens': [], 'heights': [], 'lmfdb_label': '7007.b4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.68806483950915051375579941710', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3761296790183010275115988341966853622', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[30, 254, 1]], 'xcoord_integral_points': [-47, 30]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [4, 0], '7': 'a', '11': [5, 0], '13': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '7007.b4'}
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ec_torsion_growth • Show schema
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id: 368400
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '7007.b4', 'torsion': [2, 4]}
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id: 368401
{'degree': 4, 'field': [-7, 0, -7, 0, 1], 'lmfdb_label': '7007.b4', 'torsion': [8]}
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id: 368405
{'degree': 8, 'field': [-19367, 11756, -11312, -889, 448, -7, 7, -4, 1], 'lmfdb_label': '7007.b4', 'torsion': [12]}
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id: 368404
{'degree': 8, 'field': [16, 0, 4, 0, -11, 0, 1, 0, 1], 'lmfdb_label': '7007.b4', 'torsion': [2, 8]}
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id: 368403
{'degree': 8, 'field': [1673, -3290, 1894, -1268, 1155, -132, 46, -2, 1], 'lmfdb_label': '7007.b4', 'torsion': [2, 8]}
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id: 368402
{'degree': 8, 'field': [3844, 2728, 968, -80, 125, 46, 2, -2, 1], 'lmfdb_label': '7007.b4', 'torsion': [4, 4]}
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id: 368406
{'degree': 16, 'field': [-89184157, 146262136, -164519928, 131736808, -74920062, 28225904, -5679562, 932028, 227788, 15140, -41902, -1652, 2457, -28, -20, -8, 1], 'lmfdb_label': '7007.b4', 'torsion': [16]}
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id: 368407
{'degree': 16, 'field': [2941033, 2914366, 16285145, -5139801, 2550566, 846296, -533345, -132501, 65743, -5910, -3161, 25, 260, -21, 11, -4, 1], 'lmfdb_label': '7007.b4', 'torsion': [2, 12]}
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ec_localdata • Show schema
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id: 143385
{'conductor': 7007, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '7007.b4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 143386
{'conductor': 7007, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '7007.b4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 143387
{'conductor': 7007, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '7007.b4', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1710312
{'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [235, 234, 90, 395], [256, 613, 83, 614], [57, 8, 228, 33], [393, 388, 390, 79], [609, 8, 608, 9], [7, 6, 610, 611]], 'adelic_image': '616.48.0.?', 'conductor': 7007, 'lmfdb_label': '7007.b4', 'prime': 0}
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id: 34633
{'conductor': 7007, 'elladic_image': '4.12.0.7', 'lmfdb_label': '7007.b4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 7007.b does not appear in ec_padic