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ec_curvedata • Show schema
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{'Ciso': '193200ep', 'Clabel': '193200ep4', 'Cnumber': 4, 'abc_quality': 1.0052648692236001, 'absD': 35209269938545920000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 19320, 'ainvs': [0, -1, 0, -337089408, -2382002258688], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 193200, 'degree': 35389440, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4960952295077644548070670009', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4], 'jinv': [66187969564358252770489, 550144842789780], 'lmfdb_iso': '193200.v', 'lmfdb_label': '193200.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -842723, 297413193], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '28.12.0-4.c.1.2', '120.12.0.?', '460.12.0.?', '552.12.0.?', '840.24.0.?', '1610.6.0.?', '2760.24.0.?', '3220.24.0.?', '3864.24.0.?', '19320.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, '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': '1.9982290927307689580894552128', 'prec': 100}, 'szpiro_ratio': 5.7939685522897175, '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, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, -1, 0, -1, 0, 2, -6, 4, -1, -2, -4, -2, -10, 4, 0, -10, 4, -6, 12, -16, 6, 8, 0, -10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 193200, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '193200.v', 'trace_hash': 850521406326366684}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00091903122501947732131940816139', 'prec': 113}, 'conductor': 193200, 'gens': [], 'heights': [], 'lmfdb_label': '193200.v1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.035234125309747387908983970036', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.56374600495595820654374352056913053902', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-10623, 0, 1]], 'xcoord_integral_points': [-10623]}
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lmfdb_label 193200.v1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 8500895
{'degree': 2, 'field': [-201, -1, 1], 'lmfdb_label': '193200.v1', 'torsion': [2, 2]}
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id: 8500897
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '193200.v1', 'torsion': [4]}
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id: 8500896
{'degree': 2, 'field': [29, -1, 1], 'lmfdb_label': '193200.v1', 'torsion': [4]}
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id: 8500898
{'degree': 4, 'field': [729, 0, 61, 0, 1], 'lmfdb_label': '193200.v1', 'torsion': [2, 4]}
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id: 8500902
{'degree': 8, 'field': [-226875, 0, -53000, 0, 1650, 0, 0, 0, 1], 'lmfdb_label': '193200.v1', 'torsion': [6]}
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id: 8500900
{'degree': 8, 'field': [115600, 0, 14560, 0, 6456, 0, -152, 0, 1], 'lmfdb_label': '193200.v1', 'torsion': [8]}
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id: 8500901
{'degree': 8, 'field': [11804116, 887008, -861644, -50456, 24549, 812, -266, -4, 1], 'lmfdb_label': '193200.v1', 'torsion': [8]}
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id: 8500899
{'degree': 8, 'field': [6472363401, 0, -6763372, 0, -160706, 0, -28, 0, 1], 'lmfdb_label': '193200.v1', 'torsion': [2, 4]}
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id: 8500904
{'degree': 16, 'field': [8495825461, 568108828, 197314428, -1392036708, 359223558, 375965808, -79693796, -36450044, 5885583, 2000688, -252324, -77100, 9938, 1316, -168, -8, 1], 'lmfdb_label': '193200.v1', 'torsion': [2, 8]}
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id: 8500907
{'degree': 16, 'field': [13689702009, 0, -3165057252, 0, 579176530, 0, 46016136, 0, 1197975, 0, 48264, 0, 2298, 0, 0, 0, 1], 'lmfdb_label': '193200.v1', 'torsion': [12]}
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id: 8500908
{'degree': 16, 'field': [27358908656, -43215765824, 44818782016, -3080910976, 1232017688, 358013496, -99484436, -16361848, 3295493, 492176, -60384, -21088, 3818, -168, 44, -8, 1], 'lmfdb_label': '193200.v1', 'torsion': [12]}
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id: 8500905
{'degree': 16, 'field': [324849841936, 0, -90394090064, 0, 9546814172, 0, -455723772, 0, 33714905, 0, -1282008, 0, 24122, 0, -236, 0, 1], 'lmfdb_label': '193200.v1', 'torsion': [2, 8]}
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id: 8500906
{'degree': 16, 'field': [82433997186489, 0, 19710492127596, 0, 200709998370, 0, -8550061272, 0, -265544985, 0, -5369432, 0, -40758, 0, 0, 0, 1], 'lmfdb_label': '193200.v1', 'torsion': [2, 6]}
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id: 8500903
{'degree': 16, 'field': [164053971739206756, 0, 293565028952232, 0, 32841099586120, 0, 24317841492, 0, 2422648109, 0, 241248, 0, 80570, 0, -12, 0, 1], 'lmfdb_label': '193200.v1', 'torsion': [4, 4]}
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ec_localdata • Show schema
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id: 4784729
{'conductor': 193200, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '193200.v1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 4784730
{'conductor': 193200, 'conductor_valuation': 1, 'discriminant_valuation': 20, 'j_denominator_valuation': 20, 'kodaira_symbol': 24, 'lmfdb_label': '193200.v1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 4784731
{'conductor': 193200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '193200.v1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 4784732
{'conductor': 193200, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '193200.v1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 4784733
{'conductor': 193200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '193200.v1', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2904239
{'adelic_gens': [[15452, 19319, 11569, 19314], [19313, 8, 19312, 9], [15128, 3, 14285, 2], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [16901, 16904, 7222, 16899], [7, 6, 19314, 19315], [2419, 2418, 7258, 16915], [11044, 1, 5543, 6], [12881, 8, 12884, 33]], 'adelic_image': '19320.48.0.?', 'conductor': 193200, 'lmfdb_label': '193200.v1', 'prime': 0}
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id: 719668
{'conductor': 193200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '193200.v1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 193200.v does not appear in ec_padic