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ec_curvedata • Show schema
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{'Ciso': '194688ci', 'Clabel': '194688ci2', 'Cnumber': 2, 'abc_quality': 0.7935250407803479, 'absD': 9743035524857856, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 624, 'ainvs': [0, 0, 0, -44616, -5975840], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 194688, 'degree': 774144, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7637507535888636025607816402', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2], 'jinv': [-170368, 169], 'lmfdb_iso': '194688.r', 'lmfdb_label': '194688.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -29, 91], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '12.12.0-4.a.1.2', '104.12.0.?', '208.24.0.?', '312.24.0.?', '624.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1521], [3, 2, 21632], [13, 98, 1152]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.87670178012922913881702217408', 'prec': 107}, 'szpiro_ratio': 3.672637494439383, '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, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, -2, -2, 0, 0, -2, 0, -4, -2, -2, 6, -6, -2, 6, 6, 8, 2, 8, -2, 14, 4, -8, -14, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 194688, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '194688.r', 'trace_hash': 1418328088003118837}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.029378225532692490129223541462', 'prec': 107}, 'conductor': 194688, 'gens': [], 'heights': [], 'lmfdb_label': '194688.r2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15791302496241762183528373788', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.63165209984967048734113495152048752679', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[260, 0, 1]], 'xcoord_integral_points': [260]}
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lmfdb_label 194688.r2 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 8560468
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [2, 2]}
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id: 8560469
{'degree': 4, 'field': [-225, 0, -6, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [4]}
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id: 8560472
{'degree': 8, 'field': [27, -732, 1512, -1660, 718, -100, 4, -4, 1], 'lmfdb_label': '194688.r2', 'torsion': [6]}
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id: 8560471
{'degree': 8, 'field': [841, 0, -716, 0, 362, 0, -4, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [2, 4]}
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id: 8560470
{'degree': 8, 'field': [7465, 1108, -1856, -1148, 480, -76, 40, -4, 1], 'lmfdb_label': '194688.r2', 'torsion': [2, 4]}
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id: 8560473
{'degree': 16, 'field': [1, 0, 0, 0, -102, 0, 0, 0, 10403, 0, 0, 0, -102, 0, 0, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [4, 4]}
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id: 8560474
{'degree': 16, 'field': [47524, 0, 406912, 0, 776656, 0, 553424, 0, 148764, 0, 6880, 0, -248, 0, -40, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [8]}
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id: 8560475
{'degree': 16, 'field': [749453, 584624, -17240, 252920, 77796, -30744, 33584, -10640, 5866, -2256, 1528, 152, 124, -40, 0, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 4821251
{'conductor': 194688, 'conductor_valuation': 7, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '194688.r2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 4821252
{'conductor': 194688, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '194688.r2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 4821253
{'conductor': 194688, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '194688.r2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2913289
{'adelic_gens': [[155, 414, 0, 623], [3, 8, 10, 27], [1, 0, 8, 1], [1, 8, 0, 1], [479, 414, 0, 623], [77, 204, 351, 623], [415, 0, 0, 623], [5, 8, 48, 77], [617, 8, 616, 9]], 'adelic_image': '624.48.0.?', 'conductor': 194688, 'lmfdb_label': '194688.r2', 'prime': 0}
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id: 724411
{'conductor': 194688, 'elladic_image': '4.6.0.5', 'lmfdb_label': '194688.r2', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 194688.r does not appear in ec_padic