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ec_curvedata • Show schema
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{'Ciso': '69696cx', 'Clabel': '69696cx3', 'Cnumber': 3, 'abc_quality': 0.9538342535176972, 'absD': 3717539273270034432, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [0, 0, 0, -454476, -72811024], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 69696, 'degree': 1474560, 'elladic_images': ['8.12.0.13'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2641480921824308982574843930', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4], 'jinv': [122657188, 43923], 'lmfdb_iso': '69696.bf', 'lmfdb_label': '69696.bf2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -104, -288], 'min_quad_twist_disc': 264, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.6', '12.12.0.h.1', '24.24.0-12.h.1.5', '88.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.7130940731346486687075099518', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.40830192929740296536075284305', 'prec': 107}, 'szpiro_ratio': 4.545800477437402, '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, -4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, -8, 0], 'aplist': [0, 0, -2, -4, 0, 6, 6, -8, 0, 6, 0, -6, -10, -8, 0, 6, 4, -2, 12, 8, -2, 4, 12, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 69696, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '69696.bf', 'trace_hash': 1340468993512187369}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.010799060014169241317817977885', 'prec': 107}, 'conductor': 69696, 'gens': [[-172, 520, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.7130940731346486687075099518', 'prec': 100}], 'lmfdb_label': '69696.bf2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.18933587073178022290496049809', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3267745636380863485982402759188940396', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-572, 0, 1]], 'xcoord_integral_points': [-572, -172]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '69696.bf2'}
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ec_torsion_growth • Show schema
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id: 3313925
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [2, 2]}
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id: 3313927
{'degree': 2, 'field': [22, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [4]}
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id: 3313926
{'degree': 2, 'field': [66, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [4]}
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id: 3313928
{'degree': 4, 'field': [121, 0, 44, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [2, 4]}
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id: 3313932
{'degree': 8, 'field': [-3267, 0, 1518, 0, -198, 0, 0, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [6]}
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id: 3313929
{'degree': 8, 'field': [-2802, 7776, -3156, -636, 292, 68, -18, -4, 1], 'lmfdb_label': '69696.bf2', 'torsion': [2, 4]}
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id: 3313930
{'degree': 8, 'field': [225, 0, 96, 0, 31, 0, 2, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [8]}
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id: 3313931
{'degree': 8, 'field': [256, 0, -32, 0, 0, 0, -2, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [8]}
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id: 3313935
{'degree': 16, 'field': [484, 0, -1716, 0, 949, 0, 1176, 0, 111, 0, 12, 0, 31, 0, 0, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [2, 8]}
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id: 3313934
{'degree': 16, 'field': [2473, -1884, 3638, -1428, 3710, -2616, 2238, -1104, 551, -60, 114, -24, 32, -12, -4, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [2, 8]}
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id: 3313936
{'degree': 16, 'field': [171396, 0, -1234008, 0, 2820132, 0, -2315952, 0, 217332, 0, -852, 0, -144, 0, -24, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [2, 6]}
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id: 3313933
{'degree': 16, 'field': [2959009, -17219076, 43278710, -16847456, 17187050, -3527520, 2792030, -354072, 299311, -30972, 23182, -1840, 1224, -100, 52, -4, 1], 'lmfdb_label': '69696.bf2', 'torsion': [4, 4]}
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id: 3313937
{'degree': 16, 'field': [23561316, 0, 30583560, 0, 19669684, 0, 1127184, 0, 98436, 0, 3404, 0, -408, 0, 0, 0, 1], 'lmfdb_label': '69696.bf2', 'torsion': [12]}
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id: 3313938
{'degree': 16, 'field': [25347249, 16559640, 6730128, 1836540, 3746520, 1732752, 1272384, 132228, 112590, -2352, 8376, -684, 404, 8, 24, -4, 1], 'lmfdb_label': '69696.bf2', 'torsion': [12]}
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ec_localdata • Show schema
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id: 1688291
{'conductor': 69696, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '69696.bf2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 1688292
{'conductor': 69696, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '69696.bf2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 1688293
{'conductor': 69696, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '69696.bf2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2125096
{'adelic_gens': [[232, 107, 235, 0], [172, 263, 65, 258], [1, 0, 8, 1], [1, 8, 0, 1], [7, 6, 258, 259], [1, 4, 4, 17], [257, 8, 256, 9], [119, 256, 212, 231], [29, 30, 86, 221]], 'adelic_image': '264.48.0.?', 'conductor': 69696, 'lmfdb_label': '69696.bf2', 'prime': 0}
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id: 290572
{'conductor': 69696, 'elladic_image': '8.12.0.13', 'lmfdb_label': '69696.bf2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 3570000
{'lmfdb_iso': '69696.bf', 'p': 5, 'prec': 20, 'unit': 17157765198037, 'val': 1}
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id: 3570001
{'lmfdb_iso': '69696.bf', 'p': 7, 'prec': 20, 'unit': 7466424185788174, 'val': 1}
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id: 3570005
{'lmfdb_iso': '69696.bf', 'p': 13, 'prec': 20, 'unit': 123194324288536161958, 'val': 1}
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id: 3570007
{'lmfdb_iso': '69696.bf', 'p': 17, 'prec': 20, 'unit': 55910613968488236202105, 'val': 1}
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id: 3569997
{'lmfdb_iso': '69696.bf', 'p': 19, 'prec': 20, 'unit': 518943789702009557465247, 'val': 1}
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id: 3570004
{'lmfdb_iso': '69696.bf', 'p': 29, 'prec': 20, 'unit': 3976535264395877131975780855, 'val': 1}
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id: 3570015
{'lmfdb_iso': '69696.bf', 'p': 37, 'prec': 20, 'unit': 369923383353721459430768482818, 'val': 1}
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id: 3570002
{'lmfdb_iso': '69696.bf', 'p': 41, 'prec': 20, 'unit': 2818281806951234139117889543139, 'val': 1}
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id: 3570003
{'lmfdb_iso': '69696.bf', 'p': 43, 'prec': 20, 'unit': 6687802120196671864004133544339, 'val': 1}
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id: 3570009
{'lmfdb_iso': '69696.bf', 'p': 53, 'prec': 20, 'unit': 244559685725719412556070809574958, 'val': 1}
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id: 3570013
{'lmfdb_iso': '69696.bf', 'p': 59, 'prec': 20, 'unit': 259782847758509922473026920197463, 'val': 1}
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id: 3570014
{'lmfdb_iso': '69696.bf', 'p': 61, 'prec': 20, 'unit': 38779138263707700873828089226759, 'val': 1}
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id: 3569999
{'lmfdb_iso': '69696.bf', 'p': 67, 'prec': 20, 'unit': 15830146679388728681270142688773912, 'val': 1}
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id: 3570012
{'lmfdb_iso': '69696.bf', 'p': 71, 'prec': 20, 'unit': 43073617616466525798449427947996124, 'val': 1}
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id: 3570010
{'lmfdb_iso': '69696.bf', 'p': 73, 'prec': 20, 'unit': 221154742819199277072114175591787178, 'val': 1}
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id: 3570006
{'lmfdb_iso': '69696.bf', 'p': 79, 'prec': 20, 'unit': 1024623381841166079515726839624593823, 'val': 1}
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id: 3570008
{'lmfdb_iso': '69696.bf', 'p': 83, 'prec': 20, 'unit': 642162679794229899958326934469814165, 'val': 1}
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id: 3570011
{'lmfdb_iso': '69696.bf', 'p': 89, 'prec': 20, 'unit': 1935903004578596332240261556001105672, 'val': 1}
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id: 3569998
{'lmfdb_iso': '69696.bf', 'p': 97, 'prec': 20, 'unit': 36036205644412917016207973325133402763, 'val': 1}