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ec_curvedata • Show schema
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{'Ciso': '50160bo', 'Clabel': '50160bo7', 'Cnumber': 7, 'abc_quality': 1.0456592169621262, 'absD': 185119849615107546387578880, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 25080, 'ainvs': [0, -1, 0, 139464280, 163197306480], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 19], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 50160, 'degree': 18579456, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7293919861225384182113281475', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [73240740785321709623685719, 45195275784938365817280], 'lmfdb_iso': '50160.bc', 'lmfdb_label': '50160.bc8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 8716517, -2549957914], 'min_quad_twist_disc': -4, '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', '12.48.0-12.g.1.4', '20.12.0-4.c.1.2', '60.96.0-60.c.3.10', '76.12.0.?', '88.12.0.?', '190.6.0.?', '228.96.0.?', '264.96.0.?', '380.24.0.?', '440.24.0.?', '570.24.0.?', '1140.192.1.?', '1320.192.1.?', '1672.24.0.?', '5016.192.1.?', '8360.48.0.?', '25080.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.0362448055625931087940960260', 'prec': 100}, 'szpiro_ratio': 6.2712490489840444, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, -1, 0, 6, 0, -1, 0], 'aplist': [0, -1, 1, 4, 1, 2, 6, -1, 0, -6, 4, 2, 6, -8, 0, -6, 0, 14, 4, 12, -10, -8, 0, -6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 50160, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '50160.bc', 'trace_hash': 926289487609110982}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00057635661115982560975732440553', 'prec': 113}, 'conductor': 50160, 'gens': [], 'heights': [], 'lmfdb_label': '50160.bc8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.035103246551471160177859848460', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3699116689412313770745454521982945237', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-1159, 0, 1]], 'xcoord_integral_points': [-1159]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '11': [3, 0], '19': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '50160.bc8'}
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ec_torsion_growth • Show schema
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id: 2437759
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [6]}
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id: 2437757
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '50160.bc8', 'torsion': [4]}
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id: 2437758
{'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '50160.bc8', 'torsion': [4]}
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id: 2437756
{'degree': 2, 'field': [24, -1, 1], 'lmfdb_label': '50160.bc8', 'torsion': [2, 2]}
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id: 2437762
{'degree': 4, 'field': [1, 8, -7, -2, 1], 'lmfdb_label': '50160.bc8', 'torsion': [12]}
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id: 2437760
{'degree': 4, 'field': [36, 0, 7, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [2, 4]}
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id: 2437763
{'degree': 4, 'field': [61, -4, 5, -2, 1], 'lmfdb_label': '50160.bc8', 'torsion': [12]}
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id: 2437761
{'degree': 4, 'field': [726, -42, 43, -2, 1], 'lmfdb_label': '50160.bc8', 'torsion': [2, 6]}
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id: 2437764
{'degree': 6, 'field': [2025, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [6]}
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id: 2437766
{'degree': 8, 'field': [3025, 0, -550, 0, -85, 0, -10, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [8]}
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id: 2437768
{'degree': 8, 'field': [4356, 0, 1272, 0, 133, 0, 2, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [2, 12]}
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id: 2437765
{'degree': 8, 'field': [164025, 0, -22300, 0, 910, 0, 20, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [2, 4]}
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id: 2437767
{'degree': 8, 'field': [2599927, 58564, -59840, 2464, -1011, -268, 94, -4, 1], 'lmfdb_label': '50160.bc8', 'torsion': [8]}
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id: 2437771
{'degree': 12, 'field': [1936, 0, 1356, 0, -1335, 0, 110, 0, 15, 0, 6, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [12]}
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id: 2437769
{'degree': 12, 'field': [5776, 0, 7692, 0, 3021, 0, 113, 0, -84, 0, -3, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [3, 6]}
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id: 2437772
{'degree': 12, 'field': [4006900, -4711500, 1993950, -541890, 171975, 32130, 10071, 0, 318, -180, -27, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [12]}
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id: 2437770
{'degree': 12, 'field': [94478400, 0, 0, 0, 0, 0, 18585, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [2, 6]}
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id: 2437777
{'degree': 16, 'field': [-1014464, 13606208, -12234992, -3095488, 2453588, -1149112, 478164, -65524, -2107, 10228, -444, -260, -442, 196, -8, -8, 1], 'lmfdb_label': '50160.bc8', 'torsion': [24]}
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id: 2437774
{'degree': 16, 'field': [2722500, 9982500, 31660750, -790350, 886495, 515260, 64795, -232560, 66471, -11942, 348, 256, -195, 6, 3, -2, 1], 'lmfdb_label': '50160.bc8', 'torsion': [2, 8]}
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id: 2437776
{'degree': 16, 'field': [25734996, 149960160, 107364696, -301753440, 211689232, -109677120, 44643748, -11655360, 1466565, 100320, -2608, -9120, 2682, 0, 4, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [2, 12]}
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id: 2437773
{'degree': 16, 'field': [69906321, 0, 30883752, 0, -1477382, 0, -536796, 0, 54155, 0, 1284, 0, -322, 0, 12, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [4, 4]}
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id: 2437778
{'degree': 16, 'field': [39850178833, -23110422016, 24486856578, -3378546044, 3270938148, -1946269368, 727248862, -63355316, 10924089, 3290456, -669518, 2988, 2232, -1288, 204, -8, 1], 'lmfdb_label': '50160.bc8', 'torsion': [24]}
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id: 2437775
{'degree': 16, 'field': [6452494110976, 0, -353195824576, 0, 5422610372, 0, 735298860, 0, -3806839, 0, -410400, 0, 3842, 0, 164, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [2, 8]}
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id: 2437779
{'degree': 18, 'field': [-518417848771267500, 0, 7857090193095000, 0, 442331157757500, 0, 18143500912425, 0, -497037709350, 0, 6151623795, 0, -43767828, 0, 183771, 0, -582, 0, 1], 'lmfdb_label': '50160.bc8', 'torsion': [18]}
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ec_localdata • Show schema
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id: 1200954
{'conductor': 50160, 'conductor_valuation': 4, 'discriminant_valuation': 18, 'j_denominator_valuation': 6, 'kodaira_symbol': -14, 'lmfdb_label': '50160.bc8', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 1200955
{'conductor': 50160, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '50160.bc8', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1200956
{'conductor': 50160, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '50160.bc8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 1200957
{'conductor': 50160, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '50160.bc8', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
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id: 1200958
{'conductor': 50160, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '50160.bc8', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1997849
{'adelic_gens': [[5241, 1048, 11036, 7229], [18809, 25056, 18798, 24791], [5032, 3, 4557, 24994], [7936, 21, 24795, 24706], [1, 12, 12, 145], [20901, 16724, 20, 12621], [9121, 24, 9132, 289], [15, 106, 23774, 15851], [25057, 24, 25056, 25], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '25080.384.5.?', 'conductor': 50160, 'lmfdb_label': '50160.bc8', 'prime': 0}
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id: 215560
{'conductor': 50160, 'elladic_image': '4.6.0.1', 'lmfdb_label': '50160.bc8', 'modell_image': '2B', 'prime': 2}
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id: 215561
{'conductor': 50160, 'elladic_image': '3.4.0.1', 'lmfdb_label': '50160.bc8', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 50160.bc does not appear in ec_padic