-
ec_curvedata • Show schema
Hide schema
{'Ciso': '8470ba', 'Clabel': '8470ba4', 'Cnumber': 4, 'abc_quality': 1.006944406521859, 'absD': 101674704435920, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 440, 'ainvs': [1, -1, 1, -2530012, 1549562831], 'analytic_rank': 0, 'bad_primes': [2, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 8470, 'degree': 122880, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1543413569328832883207688098', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 4], 'jinv': [1010962818911303721, 57392720], 'lmfdb_iso': '8470.z', 'lmfdb_label': '8470.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -20909, -1158507], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '10.6.0.a.1', '20.12.0.g.1', '40.24.0-20.g.1.5', '44.12.0-4.c.1.1', '88.24.0.?', '220.24.0.?', '440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.95539372053369801628979702082', 'prec': 103}, 'szpiro_ratio': 6.174595516406476, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
-
ec_classdata • Show schema
Hide schema
{'anlist': [0, 1, 1, 0, 1, 1, 0, -1, 1, -3, 1, 0, 0, 6, -1, 0, 1, 2, -3, 4, 1], 'aplist': [1, 0, 1, -1, 0, 6, 2, 4, -4, -6, 0, -2, 6, 4, 4, -2, 12, 2, -8, -8, 10, 8, 12, 10, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 8470, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '8470.z', 'trace_hash': 1284131491870043763}
-
ec_mwbsd • Show schema
Hide schema
{'area': {'__RealLiteral__': 0, 'data': '0.013451257083213623867878464489', 'prec': 107}, 'conductor': 8470, 'gens': [], 'heights': [], 'lmfdb_label': '8470.z1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.44947334307635948303224896625', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5957867446108758642579917299872846759', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[3675, -3679, 2]], 'xcoord_integral_points': []}
-
ec_iwasawa • Show schema
Hide schema
{'iwdata': {'2': [3, 0], '5': [1, 0], '7': [0, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '8470.z1'}
-
ec_torsion_growth • Show schema
Hide schema
-
id: 444030
{'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [4]}
-
id: 444029
{'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [4]}
-
id: 444028
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '8470.z1', 'torsion': [2, 2]}
-
id: 444032
{'degree': 4, 'field': [5, 0, -8, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [8]}
-
id: 444031
{'degree': 4, 'field': [89, 24, -23, -2, 1], 'lmfdb_label': '8470.z1', 'torsion': [2, 4]}
-
id: 444036
{'degree': 8, 'field': [-1920, 12480, 2880, 4128, 216, -84, -48, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [6]}
-
id: 444035
{'degree': 8, 'field': [81, 0, -180, 0, 107, 0, -20, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [2, 8]}
-
id: 444033
{'degree': 8, 'field': [58391, -7948, 7512, 860, -399, -40, 18, -4, 1], 'lmfdb_label': '8470.z1', 'torsion': [2, 4]}
-
id: 444034
{'degree': 8, 'field': [960400, 0, 0, 0, -735, 0, 0, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [8]}
-
id: 444040
{'degree': 16, 'field': [15427120, 23177080, 3429815, 10136610, -4078075, 1177610, -1398626, 78516, -89600, 12570, 5422, 274, 338, 0, 5, -4, 1], 'lmfdb_label': '8470.z1', 'torsion': [2, 6]}
-
id: 444041
{'degree': 16, 'field': [23956750, -10068300, -8899240, 9805026, -1095530, -2178660, 780959, 229944, -250556, 71082, -6115, -1980, 391, 0, -22, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [12]}
-
id: 444037
{'degree': 16, 'field': [27352900, 0, -18722400, 0, 4870260, 0, -538260, 0, 10141, 0, -156, 0, 486, 0, 24, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [4, 4]}
-
id: 444039
{'degree': 16, 'field': [150062500, 0, -222950000, 0, 106256500, 0, -16714600, 0, 508705, 0, -82120, 0, -1172, 0, -80, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [16]}
-
id: 444042
{'degree': 16, 'field': [3994240000, 0, -2508032000, 0, 555510400, 0, -56651900, 0, 3032200, 0, -119660, 0, 4705, 0, -110, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [12]}
-
id: 444038
{'degree': 16, 'field': [917472575881, -133645181740, 22021599122, 871841040, -1280756552, -33572000, -58245666, 3367000, 2421285, -33600, 14354, -560, -1412, -140, 12, 0, 1], 'lmfdb_label': '8470.z1', 'torsion': [2, 8]}
-
ec_localdata • Show schema
Hide schema
-
id: 176924
{'conductor': 8470, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '8470.z1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
-
id: 176925
{'conductor': 8470, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8470.z1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
-
id: 176926
{'conductor': 8470, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8470.z1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
-
id: 176927
{'conductor': 8470, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '8470.z1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
-
ec_galrep • Show schema
Hide schema
-
id: 1720109
{'adelic_gens': [[268, 1, 111, 6], [1, 0, 8, 1], [119, 432, 36, 407], [433, 8, 432, 9], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 434, 435], [59, 56, 298, 61], [59, 58, 178, 395]], 'adelic_image': '440.48.0.?', 'conductor': 8470, 'lmfdb_label': '8470.z1', 'prime': 0}
-
id: 41645
{'conductor': 8470, 'elladic_image': '8.12.0.6', 'lmfdb_label': '8470.z1', 'modell_image': '2B', 'prime': 2}
-
lmfdb_iso 8470.z does not appear in ec_padic