-
ec_curvedata • Show schema
Hide schema
{'Ciso': '12870bc', 'Clabel': '12870bc4', 'Cnumber': 4, 'abc_quality': 1.0625410991773636, 'absD': 138276458878458829500000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 3432, 'ainvs': [1, -1, 0, -31943899899, 2197513725059205], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 12870, 'degree': 19353600, 'elladic_images': ['2.3.0.1', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.3804280624204454681037150950', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4944928228995290413834018379264689, 189679641808585500000], 'lmfdb_iso': '12870.o', 'lmfdb_label': '12870.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3549322211, -81389397224415], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '6.24.0-6.a.1.4', '88.6.0.?', '156.48.0.?', '264.48.0.?', '3432.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7567275930607314819840893270', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.8311219180863906224060924765', 'prec': 100}, 'szpiro_ratio': 8.895532012268301, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
-
ec_classdata • Show schema
Hide schema
{'anlist': [0, 1, -1, 0, 1, 1, 0, -4, -1, 0, -1, 1, 0, 1, 4, 0, 1, 0, 0, 2, 1], 'aplist': [-1, 0, 1, -4, 1, 1, 0, 2, -6, -6, 2, -4, 6, 8, 0, 0, 12, 2, 8, -12, 8, 8, -12, -6, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 12870, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '12870.o', 'trace_hash': 1952056521858023220}
-
ec_mwbsd • Show schema
Hide schema
{'area': {'__RealLiteral__': 0, 'data': '0.00015675035325382089514089071984', 'prec': 113}, 'conductor': 12870, 'gens': [[108301, 2813357, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.7567275930607314819840893270', 'prec': 100}], 'lmfdb_label': '12870.o1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.055522108305708984692491320708', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1692425352320681620208988805549706753', 'prec': 130}, 'tamagawa_product': 432, 'torsion_generators': [[96081, 3861222, 1]], 'xcoord_integral_points': [96081, 103231, 108301]}
-
ec_iwasawa • Show schema
Hide schema
{'iwdata': {'2': [3, 0], '3': 'a', '5': [2, 0], '7': [1, 0], '11': [2, 0], '13': [2, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '12870.o1'}
-
ec_torsion_growth • Show schema
Hide schema
-
id: 663647
{'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '12870.o1', 'torsion': [2, 6]}
-
id: 663648
{'degree': 4, 'field': [198, 0, -21, 0, 1], 'lmfdb_label': '12870.o1', 'torsion': [12]}
-
id: 663649
{'degree': 6, 'field': [12, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '12870.o1', 'torsion': [3, 6]}
-
id: 663650
{'degree': 8, 'field': [55038, -65076, 33262, -8448, 1095, -44, -6, 0, 1], 'lmfdb_label': '12870.o1', 'torsion': [2, 12]}
-
id: 663651
{'degree': 8, 'field': [2722500, 0, -6534000, 0, 91300, 0, -440, 0, 1], 'lmfdb_label': '12870.o1', 'torsion': [2, 12]}
-
id: 663652
{'degree': 9, 'field': [492668028, -256670316, 42930324, -2204970, 55404, -9558, -1659, 171, 0, 1], 'lmfdb_label': '12870.o1', 'torsion': [18]}
-
id: 663653
{'degree': 12, 'field': [113635600, 0, -30747552, 0, 3521760, 0, -212936, 0, 7260, 0, -132, 0, 1], 'lmfdb_label': '12870.o1', 'torsion': [6, 6]}
-
id: 663654
{'degree': 16, 'field': [289928402500, 0, 34178749000, 0, 2244078100, 0, -13469720, 0, -2772539, 0, -91586, 0, 478, 0, 46, 0, 1], 'lmfdb_label': '12870.o1', 'torsion': [24]}
-
id: 663655
{'degree': 18, 'field': [8111844087935888, -23903017720327296, 27259465259134656, -14800659970022160, 3386031840323640, -88204068912096, -33977438250756, 3460199113872, -488621893716, 47351189820, -2148253272, 230860548, -8427201, -237582, -17595, -3318, 144, 0, 1], 'lmfdb_label': '12870.o1', 'torsion': [2, 18]}
-
ec_localdata • Show schema
Hide schema
-
id: 279245
{'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '12870.o1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
-
id: 279246
{'conductor': 12870, 'conductor_valuation': 2, 'discriminant_valuation': 16, 'j_denominator_valuation': 10, 'kodaira_symbol': -14, 'lmfdb_label': '12870.o1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
-
id: 279247
{'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '12870.o1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
-
id: 279248
{'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '12870.o1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
-
id: 279249
{'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '12870.o1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
-
ec_galrep • Show schema
Hide schema
-
id: 1749410
{'adelic_gens': [[2506, 3, 2157, 3424], [2641, 12, 2118, 73], [1002, 1585, 2717, 3290], [11, 2, 3382, 3423], [1, 0, 12, 1], [1, 6, 6, 37], [3421, 12, 3420, 13], [10, 3, 1689, 3424], [1, 12, 0, 1], [2287, 3420, 566, 3359]], 'adelic_image': '3432.96.1.?', 'conductor': 12870, 'lmfdb_label': '12870.o1', 'prime': 0}
-
id: 61178
{'conductor': 12870, 'elladic_image': '2.3.0.1', 'lmfdb_label': '12870.o1', 'modell_image': '2B', 'prime': 2}
-
id: 61179
{'conductor': 12870, 'elladic_image': '3.8.0.1', 'lmfdb_label': '12870.o1', 'modell_image': '3B.1.1', 'prime': 3}
-
ec_padic • Show schema
Hide schema
-
id: 565090
{'lmfdb_iso': '12870.o', 'p': 7, 'prec': 20, 'unit': 7636094009951184, 'val': 1}
-
id: 565086
{'lmfdb_iso': '12870.o', 'p': 19, 'prec': 20, 'unit': 64558358287979373141044, 'val': 1}
-
id: 565097
{'lmfdb_iso': '12870.o', 'p': 23, 'prec': 20, 'unit': 33162597767416684152676190, 'val': 1}
-
id: 565093
{'lmfdb_iso': '12870.o', 'p': 29, 'prec': 20, 'unit': 1910372685451595068550208189, 'val': 1}
-
id: 565102
{'lmfdb_iso': '12870.o', 'p': 31, 'prec': 20, 'unit': 10236833727072231728247297594, 'val': 1}
-
id: 565089
{'lmfdb_iso': '12870.o', 'p': 37, 'prec': 20, 'unit': 529411474987419138997044139796, 'val': 1}
-
id: 565091
{'lmfdb_iso': '12870.o', 'p': 41, 'prec': 20, 'unit': 3311548339898026204552241662916, 'val': 1}
-
id: 565092
{'lmfdb_iso': '12870.o', 'p': 43, 'prec': 20, 'unit': 6478831592262174221595007288809, 'val': 1}
-
id: 565100
{'lmfdb_iso': '12870.o', 'p': 59, 'prec': 20, 'unit': 1791536472840902403261900615938314, 'val': 1}
-
id: 565101
{'lmfdb_iso': '12870.o', 'p': 61, 'prec': 20, 'unit': 7924747162422330991985602385254740, 'val': 1}
-
id: 565088
{'lmfdb_iso': '12870.o', 'p': 67, 'prec': 20, 'unit': 536725650858500025631730953964762, 'val': 1}
-
id: 565099
{'lmfdb_iso': '12870.o', 'p': 71, 'prec': 20, 'unit': 78823760182882960246770131107979046, 'val': 1}
-
id: 565096
{'lmfdb_iso': '12870.o', 'p': 73, 'prec': 20, 'unit': 127117589463930294906479168925177396, 'val': 1}
-
id: 565094
{'lmfdb_iso': '12870.o', 'p': 79, 'prec': 20, 'unit': 616444354257957090642565897781129188, 'val': 1}
-
id: 565095
{'lmfdb_iso': '12870.o', 'p': 83, 'prec': 20, 'unit': 2346515977370074581106445491373291678, 'val': 1}
-
id: 565098
{'lmfdb_iso': '12870.o', 'p': 89, 'prec': 20, 'unit': 9525857172235314580628864228474429130, 'val': 1}
-
id: 565087
{'lmfdb_iso': '12870.o', 'p': 97, 'prec': 20, 'unit': 38638862340823749109367508132806982300, 'val': 1}