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ec_curvedata • Show schema
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{'Ciso': '248430ec', 'Clabel': '248430ec5', 'Cnumber': 5, 'abc_quality': 1.0369284989490737, 'absD': 1788788143929150, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 21840, 'ainvs': [1, 0, 1, -139120973, 631580989106], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 248430, 'degree': 28311552, 'elladic_images': ['16.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9921871827325569740408471406', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 106, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [524388516989299201, 3150], 'lmfdb_iso': '248430.ec', 'lmfdb_label': '248430.ec1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -16800, -845133], 'min_quad_twist_disc': -91, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0.e.1', '56.24.0.bh.1', '104.24.0.?', '112.48.0.?', '120.24.0.?', '208.48.0.?', '240.48.0.?', '364.12.0.?', '728.48.0.?', '840.48.0.?', '1456.96.0.?', '1560.48.0.?', '1680.96.1.?', '3120.96.0.?', '10920.96.0.?', '21840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '7.2020294771326450637011896255', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.73675742947413195346142704810', 'prec': 103}, 'szpiro_ratio': 5.462981809747271, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 1, 1, 1, -1, 0, -1, 1, -1, -4, 1, 0, 0, 1, 1, -2, -1, -4, 1], 'aplist': [-1, 1, 1, 0, -4, 0, -2, -4, -8, 6, -8, 2, 2, -12, -8, 6, 4, 2, -12, -8, -14, 0, 12, 2, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 248430, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '248430.ec', 'trace_hash': 1543100293822054192}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0025177884412272080052249649092', 'prec': 110}, 'conductor': 248430, 'gens': [[6810, -3443, 1], [6920, 12342, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.1941560364658069960411151504', 'prec': 100}, {'__RealLiteral__': 0, 'data': '3.2868606281044484860760851373', 'prec': 100}], 'lmfdb_label': '248430.ec1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.22910144231749578671779299490', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '13.199962726593672193400711030606833513', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[27239, -27243, 2]], 'xcoord_integral_points': [6810, 6920, 8880, 11922]}
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lmfdb_label 248430.ec1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 10695160
{'degree': 2, 'field': [-91, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [4]}
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id: 10695161
{'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [4]}
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id: 10695159
{'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [2, 2]}
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id: 10695162
{'degree': 4, 'field': [9, 0, -20, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [2, 4]}
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id: 10695163
{'degree': 4, 'field': [361, 0, -53, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [8]}
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id: 10695164
{'degree': 4, 'field': [2025, 0, -300, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [8]}
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id: 10695169
{'degree': 8, 'field': [-765840, -150315, 147210, 6209, -3101, -7, 7, -4, 1], 'lmfdb_label': '248430.ec1', 'torsion': [6]}
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id: 10695168
{'degree': 8, 'field': [-166319, -401760, -248416, 9360, 20181, -180, -286, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [16]}
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id: 10695166
{'degree': 8, 'field': [3952, 11648, 7088, -2240, 348, -112, -12, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [8]}
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id: 10695167
{'degree': 8, 'field': [4356, 0, -15240, 0, 2368, 0, -100, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [2, 8]}
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id: 10695165
{'degree': 8, 'field': [10449100, 2780400, 467400, 16800, -6064, -840, 12, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [2, 4]}
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id: 10695171
{'degree': 16, 'field': [61009, -359632, 1059968, -1428336, 742018, 609000, 238336, -9632, 18695, 6776, 1568, -896, -138, -56, 0, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [2, 8]}
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id: 10695176
{'degree': 16, 'field': [3326976, 0, 7016832, 0, 1927296, 0, -2819936, 0, 328496, 0, -16184, 0, 1036, 0, -52, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [12]}
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id: 10695174
{'degree': 16, 'field': [29942784, 0, 73155744, 0, 90192132, 0, -33495192, 0, 3507960, 0, -189068, 0, 5268, 0, -84, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [2, 6]}
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id: 10695173
{'degree': 16, 'field': [10325397796, -1944261984, -15889556368, -578054176, 6456720824, 433082976, -1033993312, -75013104, 75145048, 5194224, -2600792, -152768, 43860, 1888, -344, -8, 1], 'lmfdb_label': '248430.ec1', 'torsion': [2, 16]}
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id: 10695175
{'degree': 16, 'field': [70968960000, 0, -25632682875, 0, 3903839550, 0, -340701481, 0, 18724367, 0, -659521, 0, 14491, 0, -182, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [12]}
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id: 10695172
{'degree': 16, 'field': [8009669088801, 1184605664760, 7085569206600, -174564981360, 1711579214856, -63473439960, 126704886840, -1294886880, 589783726, -23905560, -29257480, 324240, 227976, -840, -760, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [16]}
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id: 10695170
{'degree': 16, 'field': [95921946300625, 25585780290000, 3412316880000, 526289190000, -70294071550, -22882410600, -2159136000, -126588000, 62820231, 8004360, 352800, -13440, -12682, -840, 0, 0, 1], 'lmfdb_label': '248430.ec1', 'torsion': [4, 4]}
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ec_localdata • Show schema
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id: 6157625
{'conductor': 248430, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '248430.ec1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 6157626
{'conductor': 248430, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '248430.ec1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 6157627
{'conductor': 248430, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '248430.ec1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 6157628
{'conductor': 248430, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '248430.ec1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 6157629
{'conductor': 248430, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '248430.ec1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 3241018
{'adelic_gens': [[1, 16, 0, 1], [21825, 16, 21824, 17], [8828, 17225, 9243, 17642], [14624, 10075, 9165, 13454], [6719, 0, 0, 21839], [15, 2, 21742, 21827], [7853, 20176, 12064, 16485], [1, 0, 16, 1], [5, 4, 21836, 21837], [19501, 20176, 17888, 16485], [11558, 17225, 11973, 17642]], 'adelic_image': '21840.192.1.?', 'conductor': 248430, 'lmfdb_label': '248430.ec1', 'prime': 0}
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id: 896847
{'conductor': 248430, 'elladic_image': '16.24.0.1', 'lmfdb_label': '248430.ec1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 248430.ec does not appear in ec_padic