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ec_curvedata • Show schema
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{'Ciso': '3872b', 'Clabel': '3872b3', 'Cnumber': 3, 'abc_quality': 1.172456969504371, 'absD': 907039232, 'ainvs': [0, 0, 0, -1331, 18634], 'analytic_rank': 0, 'bad_primes': [2, 11], 'class_deg': 4, 'class_size': 4, 'cm': -16, 'conductor': 3872, 'degree': 1440, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.58156189104762106319592882714', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4], 'jinv': [287496, 1], 'lmfdb_iso': '3872.f', 'lmfdb_label': '3872.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -11, -14], 'min_quad_twist_disc': -11, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 121], [11, 62, 32]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1372461307715231908979670529', 'prec': 103}, 'szpiro_ratio': 4.017981506837876, '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, -2, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, -2, 0, 0, -6, -2, 0, 0, 10, 0, -2, -10, 0, 0, 14, 0, 10, 0, 0, 6, 0, 0, 10, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 3872, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3872.f', 'trace_hash': 1630781610106707576}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.31250844627365331034045889908', 'prec': 103}, 'conductor': 3872, 'gens': [], 'heights': [], 'lmfdb_label': '3872.f2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.5811601975097989680370686073', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.79058009875489948401853430364932935598', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[22, 0, 1]], 'xcoord_integral_points': [22]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '3872.f2'}
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ec_torsion_growth • Show schema
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id: 201556
{'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [4]}
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id: 201557
{'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [4]}
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id: 201555
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 2]}
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id: 201558
{'degree': 4, 'field': [25, 0, -12, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 4]}
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id: 201562
{'degree': 8, 'field': [-1487, -3004, -1166, 284, -164, -16, 10, -4, 1], 'lmfdb_label': '3872.f2', 'torsion': [6]}
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id: 201560
{'degree': 8, 'field': [49, 0, -432, 0, 180, 0, -24, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 8]}
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id: 201561
{'degree': 8, 'field': [324, 0, -180, 0, 50, 0, -10, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [8]}
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id: 201559
{'degree': 8, 'field': [324, 0, 0, 0, -14, 0, 0, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 4]}
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id: 201563
{'degree': 8, 'field': [4706, -3404, 656, 200, -4, -20, 2, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [10]}
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id: 201572
{'degree': 16, 'field': [-7898, 13860, 4280, -15768, 3556, 7020, -6994, -1224, 4903, -144, -1690, 96, 304, -12, -28, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [12]}
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id: 201565
{'degree': 16, 'field': [521, -2044, 2452, 3412, -8540, -784, 11104, -1932, -6779, 2040, 2012, -852, -222, 140, 0, -8, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 8]}
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id: 201564
{'degree': 16, 'field': [6561, 0, -14580, 0, 16200, 0, -12600, 0, 6079, 0, -1400, 0, 200, 0, -20, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [4, 4]}
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id: 201573
{'degree': 16, 'field': [8633, 11240, 24370, 21692, 19998, 13004, 8642, 3644, 3503, 404, 1050, -36, 188, -8, 20, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [20]}
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id: 201571
{'degree': 16, 'field': [35641, 66836, 20596, -44000, -31658, 16816, 13920, -5520, -1820, -484, 1548, -712, 202, -88, 36, -8, 1], 'lmfdb_label': '3872.f2', 'torsion': [20]}
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id: 201568
{'degree': 16, 'field': [287422, 304584, 515396, 494400, 350152, 255912, 111716, 64008, 17524, 5388, -1336, -552, -386, -72, -4, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 6]}
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id: 201567
{'degree': 16, 'field': [343501, 1451764, 1894326, 400260, -1036782, -1125440, -435766, 20084, -3622, -4644, -3686, 140, 218, -40, 6, -4, 1], 'lmfdb_label': '3872.f2', 'torsion': [10]}
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id: 201570
{'degree': 16, 'field': [727609, 0, -1323116, 0, 835276, 0, -293372, 0, 65170, 0, -9356, 0, 844, 0, -44, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [12]}
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id: 201569
{'degree': 16, 'field': [1429921, 1593188, -955844, -1566944, 223582, 704992, -18720, -187632, 940, 31580, -444, -3496, 202, 200, -12, -8, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 10]}
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id: 201566
{'degree': 16, 'field': [7786981, 6245284, 1577594, 905460, 1740158, 39044, -89942, 111696, 14347, -17508, 3562, 568, -628, 60, 8, -4, 1], 'lmfdb_label': '3872.f2', 'torsion': [3, 6]}
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ec_localdata • Show schema
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id: 71943
{'conductor': 3872, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '3872.f2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 71944
{'conductor': 3872, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '3872.f2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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lmfdb_label 3872.f2 does not appear in ec_galrep
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lmfdb_iso 3872.f does not appear in ec_padic