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ec_curvedata • Show schema
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{'Ciso': '6720ci', 'Clabel': '6720ci1', 'Cnumber': 1, 'abc_quality': 1.0638597912103416, 'absD': 3810240, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 1, 0, -79380, -8634762], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6720, 'degree': 15360, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1636834470806870687954653800', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 52, 'isogeny_degrees': [1, 2, 4], 'jinv': [864335783029582144, 59535], 'lmfdb_iso': '6720.ca', 'lmfdb_label': '6720.ca3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -317521, -68760575], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '24.24.0-24.bb.1.14', '40.24.0-40.bb.1.13', '60.12.0.h.1', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.81710985680071441408684931927', 'prec': 103}, 'szpiro_ratio': 5.158337505060743, '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, -1, 0, 1, 0, -4, 0, 6, 0, 1, 0, 6, 0, 0, 0], 'aplist': [0, 1, 1, -1, -4, 6, 6, 0, -4, 6, 0, -2, 2, -4, 4, 6, -12, 10, -4, 8, -14, 8, 12, -6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 6720, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '6720.ca', 'trace_hash': 2006039470077520729}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.097552274673192774302923679007', 'prec': 107}, 'conductor': 6720, 'gens': [], 'heights': [], 'lmfdb_label': '6720.ca3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.28442733042249316735895307547', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8442733042249316735895307546537231693', 'prec': 130}, 'tamagawa_product': 10, 'torsion_generators': [[-163, 0, 1]], 'xcoord_integral_points': [-163]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 0], '5': [3, 0], '7': [0, 0]}, 'iwp0': 7, 'lmfdb_label': '6720.ca3'}
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ec_torsion_growth • Show schema
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id: 353870
{'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [2, 2]}
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id: 353871
{'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [4]}
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id: 353872
{'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [4]}
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id: 353873
{'degree': 4, 'field': [1, 0, 8, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [2, 4]}
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id: 353874
{'degree': 4, 'field': [60, 0, -12, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [8]}
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id: 353878
{'degree': 8, 'field': [-3, 0, 1952, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [6]}
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id: 353877
{'degree': 8, 'field': [121, 0, 436, 0, 222, 0, 4, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [2, 8]}
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id: 353875
{'degree': 8, 'field': [139876, 0, -4804, 0, -1059, 0, -4, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [2, 4]}
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id: 353876
{'degree': 8, 'field': [540225, 0, 0, 0, 3430, 0, 0, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [8]}
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id: 353882
{'degree': 16, 'field': [9, 0, -89994432, 0, -30480740, 0, -2903424, 0, -11490, 0, 3904, 0, -372, 0, 0, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [2, 6]}
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id: 353884
{'degree': 16, 'field': [4112784, 0, -4672512, 0, -381440, 0, 1391616, 0, 402600, 0, 33024, 0, 768, 0, 0, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [12]}
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id: 353879
{'degree': 16, 'field': [19069600, -44704000, 39413600, -16010000, 3025370, -94580, -99870, -61500, 48241, -8688, 5082, -1280, 536, -140, 8, -4, 1], 'lmfdb_label': '6720.ca3', 'torsion': [4, 4]}
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id: 353883
{'degree': 16, 'field': [113103225, 0, 114822000, 0, 17038900, 0, -1481136, 0, -206418, 0, 16144, 0, 996, 0, 48, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [12]}
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id: 353880
{'degree': 16, 'field': [236844490, 292813600, -30045940, -111958480, 18379466, -3946240, 10671612, -1904436, 322339, 95196, 29364, -9652, 1562, -28, 44, -8, 1], 'lmfdb_label': '6720.ca3', 'torsion': [2, 8]}
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id: 353881
{'degree': 16, 'field': [2774449233, 7815508560, 10950469056, 6708608352, 2694824820, 767393712, 145792800, 25837632, 2250006, -61968, 15168, -17568, 2580, -240, 96, 0, 1], 'lmfdb_label': '6720.ca3', 'torsion': [16]}
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ec_localdata • Show schema
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id: 137006
{'conductor': 6720, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '6720.ca3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 137007
{'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '6720.ca3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
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id: 137008
{'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6720.ca3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 137009
{'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6720.ca3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1708305
{'adelic_gens': [[113, 8, 112, 9], [7, 6, 114, 115], [37, 42, 70, 13], [1, 0, 8, 1], [28, 1, 71, 6], [1, 4, 4, 17], [104, 37, 101, 72], [1, 8, 0, 1], [88, 3, 85, 2]], 'adelic_image': '120.48.0.?', 'conductor': 6720, 'lmfdb_label': '6720.ca3', 'prime': 0}
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id: 33173
{'conductor': 6720, 'elladic_image': '8.12.0.6', 'lmfdb_label': '6720.ca3', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 6720.ca does not appear in ec_padic