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ec_curvedata • Show schema
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{'Ciso': '675a', 'Clabel': '675a2', 'Cnumber': 2, 'absD': 307546875, 'ainvs': [0, 0, 1, 0, -844], 'analytic_rank': 1, 'bad_primes': [3, 5], 'class_deg': 27, 'class_size': 4, 'cm': -3, 'conductor': 675, 'degree': 144, 'elladic_images': ['27.972.55.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.30756074429009454085694439845', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 4, 'isogeny_degrees': [1, 3, 9], 'jinv': [0, 1], 'lmfdb_iso': '675.e', 'lmfdb_label': '675.e3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 0], 'min_quad_twist_disc': -15, 'modell_images': ['3Cs'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2167732609229170786542795935', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 4.14428990242478, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, -5, 0, 0, 4, 0, 0, -7, 0], 'aplist': [0, 0, 0, 1, 0, -5, 0, -7, 0, 0, -4, -11, 0, -8, 0, 0, 0, -1, -5, 0, 7, 17, 0, 0, 19], 'class_deg': 27, 'class_size': 4, 'conductor': 675, 'isogeny_matrix': [[1, 27, 3, 9], [27, 1, 9, 3], [3, 9, 1, 3], [9, 3, 3, 1]], 'lmfdb_iso': '675.e', 'trace_hash': 1896385657987878097}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.54057521760417964272308686803', 'prec': 103}, 'conductor': 675, 'gens': [[10, 12, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2167732609229170786542795935', 'prec': 100}], 'lmfdb_label': '675.e3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.79006486746470842065100100801', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9226596102513311187457582055667422606', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [10, 124]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 7, 0], '3': 'a', '5': 'a', '7': [3, 0], '11': [3, 1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '675.e3'}
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ec_torsion_growth • Show schema
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id: 31220
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '675.e3', 'torsion': [3]}
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id: 31221
{'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '675.e3', 'torsion': [3]}
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id: 31222
{'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '675.e3', 'torsion': [2]}
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id: 31223
{'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '675.e3', 'torsion': [3, 3]}
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id: 31226
{'degree': 6, 'field': [-4, 0, 0, -8, 0, 0, 1], 'lmfdb_label': '675.e3', 'torsion': [6]}
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id: 31224
{'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '675.e3', 'torsion': [2, 2]}
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id: 31227
{'degree': 6, 'field': [4, 12, 18, 5, -3, -3, 1], 'lmfdb_label': '675.e3', 'torsion': [6]}
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id: 31225
{'degree': 6, 'field': [19, -12, 9, -4, 6, 0, 1], 'lmfdb_label': '675.e3', 'torsion': [9]}
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id: 31229
{'degree': 12, 'field': [1, 0, 0, 4, 0, 0, 17, 0, 0, -4, 0, 0, 1], 'lmfdb_label': '675.e3', 'torsion': [3, 9]}
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id: 31231
{'degree': 12, 'field': [1, 3, -9, -20, 45, 33, -70, -33, 45, 20, -9, -3, 1], 'lmfdb_label': '675.e3', 'torsion': [6, 6]}
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id: 31228
{'degree': 12, 'field': [46, -1056, 492, -3844, 5550, -3768, 1476, -300, 42, -22, 18, -6, 1], 'lmfdb_label': '675.e3', 'torsion': [4]}
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id: 31230
{'degree': 12, 'field': [2401, 0, 0, -203, 0, 0, 168, 0, 0, -8, 0, 0, 1], 'lmfdb_label': '675.e3', 'torsion': [7]}
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id: 31232
{'degree': 18, 'field': [-1, 0, 0, 24, 0, 0, -18, 0, 0, -148, 0, 0, -117, 0, 0, -12, 0, 0, 1], 'lmfdb_label': '675.e3', 'torsion': [9]}
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id: 31233
{'degree': 18, 'field': [1536, 0, 1152, -1728, 1440, -1440, 912, -324, -162, -135, 558, -747, 723, -549, 330, -144, 45, -9, 1], 'lmfdb_label': '675.e3', 'torsion': [18]}
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ec_localdata • Show schema
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id: 8276
{'conductor': 675, 'conductor_valuation': 3, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '675.e3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 8277
{'conductor': 675, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '675.e3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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{'conductor': 675, 'elladic_image': '27.972.55.16', 'lmfdb_label': '675.e3', 'modell_image': '3Cs', 'prime': 3}
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ec_padic • Show schema
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id: 12202
{'lmfdb_iso': '675.e', 'p': 7, 'prec': 20, 'unit': 40583320032632046, 'val': 0}
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id: 12205
{'lmfdb_iso': '675.e', 'p': 13, 'prec': 20, 'unit': 1175909810038434637470, 'val': 1}
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id: 12207
{'lmfdb_iso': '675.e', 'p': 19, 'prec': 20, 'unit': 1311937034380217404088128, 'val': 1}
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id: 12209
{'lmfdb_iso': '675.e', 'p': 31, 'prec': 20, 'unit': 16302933945655840652895334717, 'val': 1}
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id: 12201
{'lmfdb_iso': '675.e', 'p': 37, 'prec': 20, 'unit': 96814967712926685340794563304, 'val': 1}
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id: 12204
{'lmfdb_iso': '675.e', 'p': 43, 'prec': 20, 'unit': 5461280021849685848268045176561, 'val': 1}
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id: 12208
{'lmfdb_iso': '675.e', 'p': 61, 'prec': 20, 'unit': 1660339836024182663332564441625755, 'val': 1}
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id: 12200
{'lmfdb_iso': '675.e', 'p': 67, 'prec': 20, 'unit': 17120359774519417154793083726901645, 'val': 1}
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id: 12203
{'lmfdb_iso': '675.e', 'p': 73, 'prec': 20, 'unit': 98643558825776988917732514904306514, 'val': 1}
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id: 12206
{'lmfdb_iso': '675.e', 'p': 79, 'prec': 20, 'unit': 595660124067450065238371593376628667, 'val': 1}
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id: 12199
{'lmfdb_iso': '675.e', 'p': 97, 'prec': 20, 'unit': 32984493958242211259718025245797501779, 'val': 1}