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ec_curvedata • Show schema
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{'Ciso': '825a', 'Clabel': '825a1', 'Cnumber': 1, 'abc_quality': 0.9416222780553999, 'absD': 81675, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 30, 'ainvs': [0, -1, 1, -23, 53], 'analytic_rank': 1, 'bad_primes': [3, 5, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 825, 'degree': 72, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.30121080929250401904572205629', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [-56197120, 3267], 'lmfdb_iso': '825.b', 'lmfdb_label': '825.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -23, 53], 'min_quad_twist_disc': 1, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0.b.1', '15.8.0-3.a.1.2', '30.16.0-6.b.1.2'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.26728146468235865198494989376', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56945046136485408147918194516', 'prec': 107}, 'szpiro_ratio': 3.1508219160769277, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -1, -2, 0, 0, 1, 0, 1, 0, -1, 2, 1, 0, 0, 4, 6, 0, -7, 0], 'aplist': [0, -1, 0, 1, -1, 1, 6, -7, -6, -6, -7, -2, -6, 1, 0, 6, 0, 5, -5, -12, -14, -4, 6, 6, -17], 'class_deg': 3, 'class_size': 2, 'conductor': 825, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '825.b', 'trace_hash': 735916545652299001}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.8265366241247271378922528945', 'prec': 100}, 'conductor': 825, 'gens': [[1, 5, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.26728146468235865198494989376', 'prec': 103}], 'lmfdb_label': '825.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '3.3747765339753457527067305386', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8040304299531682383269905693733767164', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [1, 3]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 2, 0], '3': [1, 0], '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '825.b1'}
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ec_torsion_growth • Show schema
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id: 38742
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '825.b1', 'torsion': [3]}
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id: 38743
{'degree': 3, 'field': [-3, -3, -1, 1], 'lmfdb_label': '825.b1', 'torsion': [2]}
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id: 38746
{'degree': 6, 'field': [1, -1, 0, -5, 0, -1, 1], 'lmfdb_label': '825.b1', 'torsion': [6]}
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id: 38744
{'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '825.b1', 'torsion': [2, 2]}
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id: 38745
{'degree': 6, 'field': [919, 17, -125, 50, 5, -3, 1], 'lmfdb_label': '825.b1', 'torsion': [3]}
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id: 38747
{'degree': 12, 'field': [-675, 0, -1750, 0, -2325, 0, -500, 0, 275, 0, -30, 0, 1], 'lmfdb_label': '825.b1', 'torsion': [4]}
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id: 38749
{'degree': 12, 'field': [1, -1, 1, 10, -5, -1, 26, -1, -5, 10, 1, -1, 1], 'lmfdb_label': '825.b1', 'torsion': [2, 6]}
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id: 38748
{'degree': 12, 'field': [8464, 11316, 7343, 3075, -1680, -849, 739, -348, 45, -15, 8, -3, 1], 'lmfdb_label': '825.b1', 'torsion': [3, 3]}
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id: 38751
{'degree': 18, 'field': [216, 432, 1584, 1476, 1200, -708, 1354, -2472, 3802, -3135, 2414, -1932, 1201, -606, 230, -69, 22, -6, 1], 'lmfdb_label': '825.b1', 'torsion': [6]}
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id: 38750
{'degree': 18, 'field': [24389, 103443, 141201, 195998, -141645, -72867, -269909, 173967, 91491, -51435, -7989, 2967, -181, 447, 75, -22, -9, -3, 1], 'lmfdb_label': '825.b1', 'torsion': [9]}
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ec_localdata • Show schema
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id: 10671
{'conductor': 825, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '825.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 10672
{'conductor': 825, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '825.b1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 10673
{'conductor': 825, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '825.b1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1669805
{'adelic_gens': [[6, 1, 13, 24], [1, 0, 6, 1], [4, 3, 9, 7], [25, 6, 24, 7], [3, 4, 8, 11], [1, 6, 0, 1], [21, 2, 10, 7]], 'adelic_image': '30.16.0.?', 'conductor': 825, 'lmfdb_label': '825.b1', 'prime': 0}
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id: 3796
{'conductor': 825, 'elladic_image': '3.4.0.1', 'lmfdb_label': '825.b1', 'modell_image': '3B', 'prime': 3}
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ec_padic • Show schema
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id: 16650
{'lmfdb_iso': '825.b', 'p': 7, 'prec': 20, 'unit': 5672537900783536, 'val': -1}
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id: 16654
{'lmfdb_iso': '825.b', 'p': 13, 'prec': 20, 'unit': 7427394886676386720493, 'val': -1}
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id: 16656
{'lmfdb_iso': '825.b', 'p': 17, 'prec': 20, 'unit': 9149377973392497044111, 'val': 1}
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id: 16646
{'lmfdb_iso': '825.b', 'p': 19, 'prec': 20, 'unit': 700657596416456686379651, 'val': 1}
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id: 16660
{'lmfdb_iso': '825.b', 'p': 23, 'prec': 20, 'unit': 20911197846509460475747909, 'val': 1}
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id: 16653
{'lmfdb_iso': '825.b', 'p': 29, 'prec': 20, 'unit': 1646410721047031068678391469, 'val': 1}
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id: 16664
{'lmfdb_iso': '825.b', 'p': 31, 'prec': 20, 'unit': 7850033828419813799483680496, 'val': 1}
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id: 16649
{'lmfdb_iso': '825.b', 'p': 37, 'prec': 20, 'unit': 68107665375322581381712161732, 'val': 1}
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id: 16651
{'lmfdb_iso': '825.b', 'p': 41, 'prec': 20, 'unit': 4185807897881650455157095647502, 'val': 1}
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id: 16652
{'lmfdb_iso': '825.b', 'p': 43, 'prec': 20, 'unit': 338726338200938737103378355371723, 'val': -1}
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id: 16658
{'lmfdb_iso': '825.b', 'p': 53, 'prec': 20, 'unit': 518451242558614001096623479905392, 'val': 1}
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id: 16663
{'lmfdb_iso': '825.b', 'p': 61, 'prec': 20, 'unit': 8174809290612657030143051505146336, 'val': 1}
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id: 16648
{'lmfdb_iso': '825.b', 'p': 67, 'prec': 20, 'unit': 23397898585215047491239536507487395, 'val': 1}
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id: 16662
{'lmfdb_iso': '825.b', 'p': 71, 'prec': 20, 'unit': 74407739861490747378423274262165067, 'val': 1}
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id: 16659
{'lmfdb_iso': '825.b', 'p': 73, 'prec': 20, 'unit': 150761841008878515007519538756121841, 'val': 1}
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id: 16655
{'lmfdb_iso': '825.b', 'p': 79, 'prec': 20, 'unit': 1113271309779367310645622951410914379, 'val': 1}
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id: 16657
{'lmfdb_iso': '825.b', 'p': 83, 'prec': 20, 'unit': 2251158960605381552104134007280965561, 'val': 1}
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id: 16661
{'lmfdb_iso': '825.b', 'p': 89, 'prec': 20, 'unit': 2148357220611369995767434155341406510, 'val': 1}
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id: 16647
{'lmfdb_iso': '825.b', 'p': 97, 'prec': 20, 'unit': 43117807187789900726509589810513974332, 'val': 1}