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ec_curvedata • Show schema
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{'Ciso': '340a', 'Clabel': '340a1', 'Cnumber': 1, 'abc_quality': 1.0232048188989848, 'absD': 1360, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 680, 'ainvs': [0, 0, 0, -28, 57], 'analytic_rank': 1, 'bad_primes': [2, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 340, 'degree': 24, 'elladic_images': ['8.12.0.22'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.45154594322339661863590019061', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [151732224, 85], 'lmfdb_iso': '340.a', 'lmfdb_label': '340.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -28, 57], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.b.1', '8.12.0-4.b.1.2', '170.6.0.?', '340.24.0.?', '680.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.43613586273374127746982884575', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.68259500341004505510831089776', 'prec': 107}, 'szpiro_ratio': 3.7073971831134007, '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, -1, 0, -4, 0, -3, 0, 2, 0, -6, 0, 0, 0, 1, 0, 0, 0], 'aplist': [0, 0, -1, -4, 2, -6, 1, 0, 0, -6, 6, -2, -6, 6, -10, -6, 0, 10, -2, 6, 6, 6, 6, -18, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 340, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '340.a', 'trace_hash': 2180603366901477212}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '2.4672196934168313793860307831', 'prec': 100}, 'conductor': 340, 'gens': [[2, 3, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.43613586273374127746982884575', 'prec': 103}], 'lmfdb_label': '340.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '4.7549194562150077844958065147', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5553431744493382651228493958474538989', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [[3, 0, 1]], 'xcoord_integral_points': [-6, 2, 3, 4]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [1, 0], '7': [3, 0], '11': [3, 0], '13': [1, 0], '17': [2, 0], '19': [1, 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': '340.a1'}
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ec_torsion_growth • Show schema
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id: 14761
{'degree': 2, 'field': [-21, -1, 1], 'lmfdb_label': '340.a1', 'torsion': [2, 2]}
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id: 14762
{'degree': 4, 'field': [26, -8, 0, -2, 1], 'lmfdb_label': '340.a1', 'torsion': [4]}
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id: 14765
{'degree': 8, 'field': [-3, 0, -36, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '340.a1', 'torsion': [6]}
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id: 14764
{'degree': 8, 'field': [1, 0, -3042, 0, -601, 0, -18, 0, 1], 'lmfdb_label': '340.a1', 'torsion': [2, 4]}
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id: 14763
{'degree': 8, 'field': [441, -42, 2, -82, 43, -6, 8, -4, 1], 'lmfdb_label': '340.a1', 'torsion': [2, 4]}
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id: 14768
{'degree': 16, 'field': [9, 0, 36504, 0, -9450, 0, 432, 0, -20625, 0, 6192, 0, -498, 0, 0, 0, 1], 'lmfdb_label': '340.a1', 'torsion': [2, 6]}
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id: 14766
{'degree': 16, 'field': [441, -3570, 14408, -36466, 62987, -75656, 62146, -31808, 6960, 2502, -2322, 952, -98, -56, 28, -8, 1], 'lmfdb_label': '340.a1', 'torsion': [4, 4]}
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id: 14767
{'degree': 16, 'field': [84100, 0, -180768, 0, 194280, 0, -105648, 0, 33000, 0, -6160, 0, 676, 0, -40, 0, 1], 'lmfdb_label': '340.a1', 'torsion': [8]}
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ec_localdata • Show schema
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id: 3316
{'conductor': 340, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '340.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
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id: 3317
{'conductor': 340, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '340.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 3318
{'conductor': 340, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '340.a1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1667222
{'adelic_gens': [[142, 1, 431, 4], [341, 8, 0, 1], [673, 8, 672, 9], [177, 6, 674, 675], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [3, 8, 28, 75], [86, 1, 103, 4], [5, 8, 48, 77]], 'adelic_image': '680.48.0.?', 'conductor': 340, 'lmfdb_label': '340.a1', 'prime': 0}
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id: 1439
{'conductor': 340, 'elladic_image': '8.12.0.22', 'lmfdb_label': '340.a1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 3990
{'lmfdb_iso': '340.a', 'p': 7, 'prec': 20, 'unit': 1318780764976827, 'val': 2}
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id: 3988
{'lmfdb_iso': '340.a', 'p': 11, 'prec': 20, 'unit': 1656525602876804560, 'val': 2}
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id: 3994
{'lmfdb_iso': '340.a', 'p': 13, 'prec': 20, 'unit': 115302874790577706250, 'val': 1}
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id: 3993
{'lmfdb_iso': '340.a', 'p': 29, 'prec': 20, 'unit': 1987838859956616484578282124, 'val': 1}
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id: 4003
{'lmfdb_iso': '340.a', 'p': 31, 'prec': 20, 'unit': 9796241290701450336761222579, 'val': 1}
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id: 3989
{'lmfdb_iso': '340.a', 'p': 37, 'prec': 20, 'unit': 596028245973225929609046205933, 'val': 1}
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id: 3991
{'lmfdb_iso': '340.a', 'p': 41, 'prec': 20, 'unit': 3035884078022512957433224861429, 'val': 1}
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id: 3992
{'lmfdb_iso': '340.a', 'p': 43, 'prec': 20, 'unit': 3282173266273884874711828620372, 'val': 1}
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id: 3995
{'lmfdb_iso': '340.a', 'p': 47, 'prec': 20, 'unit': 27004718196967258820545113233465, 'val': 1}
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id: 3997
{'lmfdb_iso': '340.a', 'p': 53, 'prec': 20, 'unit': 425743116202012860851026378968485, 'val': 1}
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id: 4002
{'lmfdb_iso': '340.a', 'p': 61, 'prec': 20, 'unit': 101675628375461292088435445817955, 'val': 1}
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id: 3996
{'lmfdb_iso': '340.a', 'p': 67, 'prec': 20, 'unit': 27530147183392060426406793529966124, 'val': 1}
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id: 4000
{'lmfdb_iso': '340.a', 'p': 71, 'prec': 20, 'unit': 97314208875318984335676279262741051, 'val': 1}
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id: 3998
{'lmfdb_iso': '340.a', 'p': 73, 'prec': 20, 'unit': 101282774597120147291358086773128481, 'val': 1}
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id: 4001
{'lmfdb_iso': '340.a', 'p': 79, 'prec': 20, 'unit': 50565040246411432264427292713968276, 'val': 1}
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id: 3987
{'lmfdb_iso': '340.a', 'p': 83, 'prec': 20, 'unit': 2469512070192069579598577556692759885, 'val': 1}
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id: 3999
{'lmfdb_iso': '340.a', 'p': 89, 'prec': 20, 'unit': 7384051877671755504022008572502607826, 'val': 1}
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id: 3986
{'lmfdb_iso': '340.a', 'p': 97, 'prec': 20, 'unit': 25256572466193956212615831864044049796, 'val': 1}