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ec_curvedata • Show schema
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{'Ciso': '3312b', 'Clabel': '3312b3', 'Cnumber': 3, 'abc_quality': 1.0860502383723558, 'absD': 1253401122816, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 552, 'ainvs': [0, 0, 0, -2739, -11950], 'analytic_rank': 0, 'bad_primes': [2, 3, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3312, 'degree': 4096, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0119645730110737635619413798', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [1522096994, 839523], 'lmfdb_iso': '3312.p', 'lmfdb_label': '3312.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -304, -544], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '12.12.0-4.c.1.2', '24.24.0-24.s.1.3', '184.24.0.?', '552.48.0.?'], '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, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.17272648683626428243481068333', 'prec': 107}, 'szpiro_ratio': 4.3625300425518985, '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, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, 2, 4, 0, -2, 2, 4, -1, 2, 8, 2, -10, 4, 0, -6, 12, 2, 12, -16, 10, 4, 0, -6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 3312, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3312.p', 'trace_hash': 1661713393460512702}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.13213526502741530254293457718', 'prec': 103}, 'conductor': 3312, 'gens': [], 'heights': [], 'lmfdb_label': '3312.p2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.70624689439015107203512489091', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8249875775606042881404995636456320013', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-50, 0, 1]], 'xcoord_integral_points': [-50]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '23': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '3312.p2'}
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ec_torsion_growth • Show schema
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id: 172703
{'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [2, 2]}
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id: 172704
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '3312.p2', 'torsion': [4]}
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id: 172705
{'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [4]}
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id: 172706
{'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [2, 4]}
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id: 172710
{'degree': 8, 'field': [-108, 0, -300, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [6]}
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id: 172707
{'degree': 8, 'field': [9, 0, 36, 0, 12, 0, -12, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [2, 4]}
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id: 172708
{'degree': 8, 'field': [36, 0, -6, 0, -5, 0, -1, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [8]}
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id: 172709
{'degree': 8, 'field': [1444, 0, 2288, 0, 708, 0, 56, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [8]}
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id: 172711
{'degree': 16, 'field': [81, 0, -324, 0, 648, 0, -864, 0, 711, 0, -288, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [4, 4]}
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id: 172712
{'degree': 16, 'field': [324, -216, -54, 300, -23, -96, 456, -212, 14, 136, -22, 4, 72, -36, 8, -4, 1], 'lmfdb_label': '3312.p2', 'torsion': [2, 8]}
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id: 172714
{'degree': 16, 'field': [4761, 0, -13356, 0, 6988, 0, 2364, 0, -1362, 0, -292, 0, 60, 0, -12, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [2, 6]}
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id: 172715
{'degree': 16, 'field': [11664, 0, -32400, 0, 86112, 0, -10800, 0, 1404, 0, -600, 0, 36, 0, 0, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [12]}
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id: 172716
{'degree': 16, 'field': [132496, 0, 215776, 0, 65776, 0, 95584, 0, 22696, 0, 136, 0, 40, 0, 16, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [12]}
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id: 172713
{'degree': 16, 'field': [131262849, 0, 75214656, 0, 15701040, 0, 1368576, 0, 62946, 0, 6336, 0, 432, 0, 0, 0, 1], 'lmfdb_label': '3312.p2', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 60129
{'conductor': 3312, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '3312.p2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 60130
{'conductor': 3312, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '3312.p2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 60131
{'conductor': 3312, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '3312.p2', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1685547
{'adelic_gens': [[97, 8, 388, 33], [208, 491, 73, 102], [1, 0, 8, 1], [480, 199, 455, 408], [1, 8, 0, 1], [1, 4, 4, 17], [176, 549, 179, 550], [7, 6, 546, 547], [545, 8, 544, 9]], 'adelic_image': '552.48.0.?', 'conductor': 3312, 'lmfdb_label': '3312.p2', 'prime': 0}
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id: 16629
{'conductor': 3312, 'elladic_image': '8.12.0.7', 'lmfdb_label': '3312.p2', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 3312.p does not appear in ec_padic