-
ec_curvedata • Show schema
Hide schema
{'Ciso': '121968fk', 'Clabel': '121968fk3', 'Cnumber': 3, 'abc_quality': 1.0728576630678985, 'absD': 7293115924074288, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 924, 'ainvs': [0, 0, 0, -123420, 17187203], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 121968, 'degree': 622080, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8164891529045933666097472852', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 87, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-10061824000, 352947], 'lmfdb_iso': '121968.dj', 'lmfdb_label': '121968.dj2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -113, -516], 'min_quad_twist_disc': -132, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.24.0.b.1', '28.6.0.b.1', '84.48.1.?', '132.48.0.?', '924.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2988131922784884352328679713', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.16281368801529518759125782940', 'prec': 107}, 'szpiro_ratio': 3.999696099682557, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
-
ec_classdata • Show schema
Hide schema
{'anlist': [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0], 'aplist': [0, 0, 0, 1, 0, -2, 0, -4, -6, 6, -8, 2, 12, -4, 12, 6, 0, 10, -8, 6, 10, -4, 12, -12, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 121968, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '121968.dj', 'trace_hash': 177230951951766925}
-
ec_mwbsd • Show schema
Hide schema
{'area': {'__RealLiteral__': 0, 'data': '0.026437328589493798758035879559', 'prec': 107}, 'conductor': 121968, 'gens': [[181, 882, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2988131922784884352328679713', 'prec': 100}], 'lmfdb_label': '121968.dj2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.41602439113662333565747439469', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.4840556102144669327197991657325080263', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-407, 0, 1]], 'xcoord_integral_points': [-407, 181]}
-
ec_iwasawa • Show schema
Hide schema
{'iwdata': {'2': 'a', '3': 'a', '5': [1, 3, 0], '7': [2, 0], '11': 'a', '13': [1, 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, 0]}, 'iwp0': 0, 'lmfdb_label': '121968.dj2'}
-
ec_torsion_growth • Show schema
Hide schema
-
id: 5571136
{'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '121968.dj2', 'torsion': [6]}
-
id: 5571135
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '121968.dj2', 'torsion': [2, 2]}
-
id: 5571137
{'degree': 4, 'field': [-94, -52, -24, -2, 1], 'lmfdb_label': '121968.dj2', 'torsion': [4]}
-
id: 5571138
{'degree': 4, 'field': [121, 0, 11, 0, 1], 'lmfdb_label': '121968.dj2', 'torsion': [2, 6]}
-
id: 5571139
{'degree': 6, 'field': [2058, 0, 0, -90, 0, 0, 1], 'lmfdb_label': '121968.dj2', 'torsion': [6]}
-
id: 5571142
{'degree': 8, 'field': [-19, 70, -22, -82, 7, 38, -8, -4, 1], 'lmfdb_label': '121968.dj2', 'torsion': [12]}
-
id: 5571140
{'degree': 8, 'field': [364, -2240, 3848, -1328, 400, -16, 32, -4, 1], 'lmfdb_label': '121968.dj2', 'torsion': [2, 4]}
-
id: 5571141
{'degree': 8, 'field': [8836, 4888, 448, 872, 566, 152, 28, -2, 1], 'lmfdb_label': '121968.dj2', 'torsion': [2, 4]}
-
id: 5571143
{'degree': 12, 'field': [562500, 0, 0, 0, 0, 0, 4968, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '121968.dj2', 'torsion': [6, 6]}
-
id: 5571146
{'degree': 16, 'field': [361, -1330, 4482, -4656, 6357, 102, 4522, 614, 2448, -888, 1128, -330, 209, -44, 24, -4, 1], 'lmfdb_label': '121968.dj2', 'torsion': [2, 12]}
-
id: 5571145
{'degree': 16, 'field': [13069, 17066, -7200, -15626, -621, 5652, 3730, -1568, -2760, 818, 910, -336, -126, 56, 12, -8, 1], 'lmfdb_label': '121968.dj2', 'torsion': [2, 12]}
-
id: 5571144
{'degree': 16, 'field': [63824121, 0, 33392976, 0, 263728, 0, -877064, 0, -270358, 0, -23504, 0, 3008, 0, -104, 0, 1], 'lmfdb_label': '121968.dj2', 'torsion': [8]}
-
id: 5571147
{'degree': 18, 'field': [-112284823, -91322868, -9389604, -62181274, 132960843, -62422332, 36797267, 13511616, -20791209, -645104, 3136926, -16458, -221612, 1440, 7947, -22, -141, 0, 1], 'lmfdb_label': '121968.dj2', 'torsion': [18]}
-
ec_localdata • Show schema
Hide schema
-
id: 3003055
{'conductor': 121968, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '121968.dj2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
-
id: 3003056
{'conductor': 121968, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '121968.dj2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
-
id: 3003057
{'conductor': 121968, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '121968.dj2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
-
id: 3003058
{'conductor': 121968, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '121968.dj2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
-
ec_galrep • Show schema
Hide schema
-
id: 2459825
{'adelic_gens': [[251, 0, 0, 923], [802, 165, 671, 428], [11, 2, 874, 915], [549, 242, 154, 439], [913, 12, 912, 13], [1, 0, 12, 1], [1, 6, 6, 37], [1, 12, 0, 1], [661, 264, 858, 661]], 'adelic_image': '924.96.1.?', 'conductor': 121968, 'lmfdb_label': '121968.dj2', 'prime': 0}
-
id: 478419
{'conductor': 121968, 'elladic_image': '2.3.0.1', 'lmfdb_label': '121968.dj2', 'modell_image': '2B', 'prime': 2}
-
id: 478420
{'conductor': 121968, 'elladic_image': '3.4.0.1', 'lmfdb_label': '121968.dj2', 'modell_image': '3B', 'prime': 3}
-
ec_padic • Show schema
Hide schema
-
id: 6379207
{'lmfdb_iso': '121968.dj', 'p': 13, 'prec': 20, 'unit': 1449017987196013674555, 'val': 1}
-
id: 6379209
{'lmfdb_iso': '121968.dj', 'p': 19, 'prec': 20, 'unit': 1170491929787674035203480, 'val': 1}
-
id: 6379212
{'lmfdb_iso': '121968.dj', 'p': 23, 'prec': 20, 'unit': 14748011712623710690808535, 'val': 1}
-
id: 6379206
{'lmfdb_iso': '121968.dj', 'p': 29, 'prec': 20, 'unit': 3022905428033886074170240022, 'val': 1}
-
id: 6379216
{'lmfdb_iso': '121968.dj', 'p': 31, 'prec': 20, 'unit': 17674505408780467261255950247, 'val': 1}
-
id: 6379202
{'lmfdb_iso': '121968.dj', 'p': 37, 'prec': 20, 'unit': 111872526137935301193287725737, 'val': 1}
-
id: 6379204
{'lmfdb_iso': '121968.dj', 'p': 41, 'prec': 20, 'unit': 1000324947667425295663208266589, 'val': 1}
-
id: 6379205
{'lmfdb_iso': '121968.dj', 'p': 43, 'prec': 20, 'unit': 3032093949221458929443777365397, 'val': 1}
-
id: 6379208
{'lmfdb_iso': '121968.dj', 'p': 47, 'prec': 20, 'unit': 44190868050406005309878662405636, 'val': 1}
-
id: 6379210
{'lmfdb_iso': '121968.dj', 'p': 53, 'prec': 20, 'unit': 506532538139203941672760159637897, 'val': 1}
-
id: 6379215
{'lmfdb_iso': '121968.dj', 'p': 61, 'prec': 20, 'unit': 7100204772238781293736477850424670, 'val': 1}
-
id: 6379201
{'lmfdb_iso': '121968.dj', 'p': 67, 'prec': 20, 'unit': 34528845877471899166135745863344701, 'val': 1}
-
id: 6379203
{'lmfdb_iso': '121968.dj', 'p': 71, 'prec': 20, 'unit': 52452112220467002099736235751616934, 'val': 1}
-
id: 6379211
{'lmfdb_iso': '121968.dj', 'p': 73, 'prec': 20, 'unit': 133964427660071829056323265852367693, 'val': 1}
-
id: 6379214
{'lmfdb_iso': '121968.dj', 'p': 79, 'prec': 20, 'unit': 424832984877967257555557646278380251, 'val': 1}
-
id: 6379200
{'lmfdb_iso': '121968.dj', 'p': 83, 'prec': 20, 'unit': 28591074904257517266284893973476367, 'val': 2}
-
id: 6379213
{'lmfdb_iso': '121968.dj', 'p': 89, 'prec': 20, 'unit': 4181899793339802982874423707746904117, 'val': 1}
-
id: 6379199
{'lmfdb_iso': '121968.dj', 'p': 97, 'prec': 20, 'unit': 18582924834815657496729456480264914794, 'val': 1}