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ec_curvedata • Show schema
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{'Ciso': '150150ct', 'Clabel': '150150ct4', 'Cnumber': 4, 'abc_quality': 0.9919358401725701, 'absD': 11743015767217046343281250, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120120, 'ainvs': [1, 1, 1, -34355213, 182167285781], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 150150, 'degree': 47775744, 'elladic_images': ['8.12.0.8', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4980411888274339750759938635', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 4, 'iso_nlabel': 101, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [-286999819333751016766729, 751553009101890965970], 'lmfdb_iso': '150150.dx', 'lmfdb_label': '150150.dx7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1374209, 1457338286], 'min_quad_twist_disc': 5, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '8.12.0-4.c.1.4', '12.24.0.g.1', '15.8.0-3.a.1.2', '24.48.0-12.g.1.13', '30.24.0-6.a.1.2', '60.48.0-12.g.1.1', '120.96.0.?', '312.96.0.?', '520.24.0.?', '924.48.0.?', '1540.12.0.?', '1560.192.1.?', '1848.96.0.?', '3080.24.0.?', '4620.96.0.?', '8008.24.0.?', '9240.192.1.?', '24024.192.1.?', '40040.48.0.?', '120120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 6, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.2873454832581871625887449850', 'prec': 100}, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.6933222326103837877756141969', 'prec': 100}, 'szpiro_ratio': 5.485153585662142, '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, 0, -1, -1, 1, 1, 0, 1, -1, -1, -1, 0, 1, 6, 1, -4, 0], 'aplist': [1, -1, 0, -1, 1, -1, 6, -4, 0, -6, 8, 10, -6, 4, 0, -6, 12, -10, -8, 12, -14, 8, 0, 6, -14], 'class_deg': 12, 'class_size': 8, 'conductor': 150150, 'isogeny_matrix': [[1, 2, 3, 4, 6, 12, 12, 4], [2, 1, 6, 2, 3, 6, 6, 2], [3, 6, 1, 12, 2, 4, 4, 12], [4, 2, 12, 1, 6, 3, 12, 4], [6, 3, 2, 6, 1, 2, 2, 6], [12, 6, 4, 3, 2, 1, 4, 12], [12, 6, 4, 12, 2, 4, 1, 3], [4, 2, 12, 4, 6, 12, 3, 1]], 'lmfdb_iso': '150150.dx', 'trace_hash': 1921803219427024507}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00091546138154091921185524429278', 'prec': 113}, 'conductor': 150150, 'gens': [[2599, 3198595, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '6.2873454832581871625887449850', 'prec': 100}], 'lmfdb_label': '150150.dx7', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.063163162915616581206875061214', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.5310870495792705557822949756932600386', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-30525, 30521, 2]], 'xcoord_integral_points': []}
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lmfdb_label 150150.dx7 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 6753421
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [4]}
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id: 6753423
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '150150.dx7', 'torsion': [6]}
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id: 6753422
{'degree': 2, 'field': [385, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [4]}
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id: 6753420
{'degree': 2, 'field': [770, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [2, 2]}
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id: 6753426
{'degree': 4, 'field': [4, 0, -6, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [12]}
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id: 6753427
{'degree': 4, 'field': [6161, -152, 153, -2, 1], 'lmfdb_label': '150150.dx7', 'torsion': [12]}
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id: 6753425
{'degree': 4, 'field': [24179, -306, 307, -2, 1], 'lmfdb_label': '150150.dx7', 'torsion': [2, 6]}
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id: 6753424
{'degree': 4, 'field': [37249, 0, 384, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [2, 4]}
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id: 6753428
{'degree': 6, 'field': [245734, 302, -2120, 905, 5, -3, 1], 'lmfdb_label': '150150.dx7', 'torsion': [6]}
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id: 6753432
{'degree': 8, 'field': [2676881, -243668, 252416, -17644, 9193, -448, 154, -4, 1], 'lmfdb_label': '150150.dx7', 'torsion': [2, 12]}
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id: 6753430
{'degree': 8, 'field': [151782400, 0, 3942400, 0, -66370, 0, -200, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [8]}
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id: 6753431
{'degree': 8, 'field': [1338131250, -132536250, -13824625, 770000, 139075, -3850, -465, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [8]}
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id: 6753429
{'degree': 8, 'field': [1423854756, 0, -905488, 0, 75484, 0, 8, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [2, 4]}
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id: 6753433
{'degree': 12, 'field': [918211204, 64179636, 10888928, 656580, -489600, -99744, 69139, -5193, 330, -15, 8, -3, 1], 'lmfdb_label': '150150.dx7', 'torsion': [3, 6]}
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id: 6753435
{'degree': 12, 'field': [60550635384, -2131684992, 367717452, -471616200, 10135030, -2438232, 1313581, -10386, 6645, -1800, 7, -6, 1], 'lmfdb_label': '150150.dx7', 'torsion': [12]}
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id: 6753436
{'degree': 12, 'field': [11564453418400, 3690178261600, 333697755600, 5360540960, 3340569640, -500945880, 12783196, -848496, 76980, 1780, 250, -6, 1], 'lmfdb_label': '150150.dx7', 'torsion': [12]}
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id: 6753434
{'degree': 12, 'field': [814467689102796, 68972366228904, 5140640054836, 52457438500, 39077048880, -1892336496, 93885371, -2075106, 341475, 1780, 481, -6, 1], 'lmfdb_label': '150150.dx7', 'torsion': [2, 6]}
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id: 6753441
{'degree': 16, 'field': [351530410000, 0, 36522640000, 0, -30813013000, 0, -4472160000, 0, -52336000, 0, 5808000, 0, -51970, 0, -80, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [24]}
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id: 6753440
{'degree': 16, 'field': [607721740011, -562393379232, 656887378860, -174233182200, 53928285880, 29469014904, 7440162072, -14800545640, 3705428525, -4866520, 2311652, -729904, 121590, 0, 20, -8, 1], 'lmfdb_label': '150150.dx7', 'torsion': [2, 12]}
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id: 6753442
{'degree': 16, 'field': [4583923820100, 0, -698421542760, 0, 49115346469, 0, -2145027402, 0, 65286431, 0, -1374492, 0, 19775, 0, -186, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [24]}
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id: 6753439
{'degree': 16, 'field': [167961600000000, 0, -12130560000000, 0, 848620800000, 0, -25744680000, 0, 713505025, 0, -7151300, 0, 65480, 0, -260, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [2, 8]}
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id: 6753438
{'degree': 16, 'field': [91054086038876416, 0, -4111798532601536, 0, 82704256164772, 0, -1013604659508, 0, 8622552945, 0, -52614072, 0, 225082, 0, -644, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [2, 8]}
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id: 6753437
{'degree': 16, 'field': [126656428693650625, 0, 0, 0, 0, 0, 0, 0, 12100199650, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '150150.dx7', 'torsion': [4, 4]}
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id: 6753443
{'degree': 18, 'field': [134387970100153936, 62759110884595968, 9308601058317456, -654585517214540, -411045002600112, -57587633647662, 52454416173, 909998865102, 81405084162, -2060697591, -488111892, 25132326, 3465975, -870864, -10206, 4400, -213, -3, 1], 'lmfdb_label': '150150.dx7', 'torsion': [18]}
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ec_localdata • Show schema
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id: 3714183
{'conductor': 150150, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '150150.dx7', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 3714184
{'conductor': 150150, 'conductor_valuation': 1, 'discriminant_valuation': 24, 'j_denominator_valuation': 24, 'kodaira_symbol': 28, 'lmfdb_label': '150150.dx7', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 3714185
{'conductor': 150150, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '150150.dx7', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 3714186
{'conductor': 150150, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '150150.dx7', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 3714187
{'conductor': 150150, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '150150.dx7', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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id: 3714188
{'conductor': 150150, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '150150.dx7', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 2638217
{'adelic_gens': [[24008, 120099, 285, 374], [15, 106, 118814, 110891], [36961, 24, 83172, 289], [1, 12, 12, 145], [120097, 24, 120096, 25], [21856, 3, 108741, 120034], [60061, 24, 40040, 20021], [115122, 95119, 25517, 6692], [1, 24, 0, 1], [30046, 21, 29745, 119746], [1, 0, 24, 1], [102976, 3, 33861, 120034]], 'adelic_image': '120120.384.5.?', 'conductor': 150150, 'lmfdb_label': '150150.dx7', 'prime': 0}
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id: 576494
{'conductor': 150150, 'elladic_image': '8.12.0.8', 'lmfdb_label': '150150.dx7', 'modell_image': '2B', 'prime': 2}
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id: 576495
{'conductor': 150150, 'elladic_image': '3.4.0.1', 'lmfdb_label': '150150.dx7', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 150150.dx does not appear in ec_padic