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ec_curvedata • Show schema
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{'Ciso': '330330bg', 'Clabel': '330330bg6', 'Cnumber': 6, 'abc_quality': 1.0265231881197245, 'absD': 43553576659081138650, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 240240, 'ainvs': [1, 1, 0, -70787, 317572479], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 7, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 330330, 'degree': 10485760, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4473864831327349181273850948', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-22143063655441, 24584858584650], 'lmfdb_iso': '330330.bg', 'lmfdb_label': '330330.bg3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -585, -238863], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '40.24.0.ca.1', '44.12.0-4.c.1.1', '88.24.0.?', '104.24.0.?', '336.24.0.?', '440.48.0.?', '520.48.0.?', '1144.48.0.?', '1680.48.0.?', '3696.48.0.?', '4368.48.0.?', '5720.96.0.?', '18480.96.0.?', '21840.96.1.?', '48048.96.0.?', '240240.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 10, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '4.0744541952506647082407767123', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1573], [3, 4, 110110], [5, 6, 66066], [7, 8, 47190], [11, 62, 2730], [13, 14, 25410]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2484388467335496460964133058', 'prec': 100}, 'szpiro_ratio': 4.145136681548175, '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, 1, -1, 1, -1, 0, -1, -1, -1, -1, 1, -2, -1, -4, 1], 'aplist': [-1, -1, 1, 1, 0, -1, -2, -4, 0, -6, -8, 6, -10, -4, 0, 6, 4, -6, -4, 0, 6, 0, -12, -6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 330330, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '330330.bg', 'trace_hash': 1874070525972424535}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0074856085166496886393718721687', 'prec': 110}, 'conductor': 330330, 'gens': [[765, 26298, 1], [-117, 18066, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8914200708025754155021986567', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.2993065580610044871132583446', 'prec': 100}], 'lmfdb_label': '330330.bg3', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.16356096776126276930984791230', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.662746740386172978804529583329532052', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-2869, 2869, 2]], 'xcoord_integral_points': [-117, 275, 765, 1733, 8213]}
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lmfdb_label 330330.bg3 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 13849511
{'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [4]}
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id: 13849510
{'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 2]}
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id: 13849512
{'degree': 2, 'field': [286, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [4]}
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id: 13849515
{'degree': 4, 'field': [16, 0, -3, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [8]}
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id: 13849513
{'degree': 4, 'field': [1369, 0, 30, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 4]}
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id: 13849514
{'degree': 4, 'field': [14161, 0, -282, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [8]}
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id: 13849519
{'degree': 8, 'field': [-11244288, 0, 2917552, 0, -11616, 0, 0, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [6]}
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id: 13849517
{'degree': 8, 'field': [10169, -3436, 3282, 296, -117, -40, 18, -4, 1], 'lmfdb_label': '330330.bg3', 'torsion': [8]}
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id: 13849516
{'degree': 8, 'field': [427131, 20692, -19338, -2720, 1391, -40, 18, -4, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 4]}
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id: 13849518
{'degree': 8, 'field': [592900, 0, 69740, 0, 3941, 0, 98, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 8]}
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id: 13849521
{'degree': 16, 'field': [881721, 0, 1684780, 0, 974830, 0, 135200, 0, -12049, 0, -520, 0, 290, 0, -20, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 8]}
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id: 13849525
{'degree': 16, 'field': [695324161, 0, 461952008, 0, 18963196, 0, -24900264, 0, 2054406, 0, -74376, 0, 3196, 0, -88, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [12]}
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id: 13849523
{'degree': 16, 'field': [63980480116, -202933358880, 206168355568, -29968357440, 22229658488, -6778430400, -831850464, -2419200, 66189065, -7505400, 1705476, -68880, 23558, -840, 148, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [16]}
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id: 13849520
{'degree': 16, 'field': [182440891161, 0, 16947877420, 0, 1674801166, 0, 44164640, 0, 2040911, 0, 11960, 0, 2786, 0, -20, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [4, 4]}
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id: 13849526
{'degree': 16, 'field': [614825746662400, 0, 78885271088000, 0, 3969892201600, 0, 109797201696, 0, 1872582192, 0, 20543016, 0, 142636, 0, 572, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [12]}
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id: 13849524
{'degree': 16, 'field': [7108297506918400, 0, -288177213833600, 0, 4812385052800, 0, 9114140256, 0, 708347952, 0, 2231736, 0, -60164, 0, 52, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 6]}
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id: 13849522
{'degree': 16, 'field': [21873460788097681, 0, 107168653888072, 0, -1442016433912, 0, -184716506496, 0, -195637570, 0, 9424824, 0, 62408, 0, -608, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [16]}
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ec_localdata • Show schema
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id: 8173518
{'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '330330.bg3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 8173519
{'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '330330.bg3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 8173520
{'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '330330.bg3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 8173521
{'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '330330.bg3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
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id: 8173522
{'conductor': 330330, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '330330.bg3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 8173523
{'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '330330.bg3', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 3730793
{'adelic_gens': [[1, 16, 0, 1], [5, 4, 240236, 240237], [15, 2, 240142, 240227], [171601, 218416, 40568, 65649], [215678, 223861, 177529, 32770], [43679, 0, 0, 240239], [80081, 218416, 29128, 65649], [114676, 223861, 98439, 32770], [1, 0, 16, 1], [120968, 43681, 124399, 152890], [91741, 218416, 12848, 130725], [240225, 16, 240224, 17]], 'adelic_image': '240240.192.1.?', 'conductor': 330330, 'lmfdb_label': '330330.bg3', 'prime': 0}
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id: 1150047
{'conductor': 330330, 'elladic_image': '8.12.0.5', 'lmfdb_label': '330330.bg3', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 330330.bg does not appear in ec_padic