Elliptic curve data - 10470.a4

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  intrinsic_torsion	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '10470a', 'Clabel': '10470a1', 'Cnumber': 1, 'abc_quality': 0.9374248464592819, 'absD': 3952292659200, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 8376, 'ainvs': [1, 1, 0, 3543, 52101], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 349], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 10470, 'degree': 31104, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1049804472956300000510713609', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [4916382075769319, 3952292659200], 'lmfdb_iso': '10470.a', 'lmfdb_label': '10470.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 3543, 52101], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '12.12.0-4.c.1.2', '24.24.0-24.ba.1.4', '1396.12.0.?', '2094.6.0.?', '2792.24.0.?', '4188.24.0.?', '8376.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.1839591098003210657698858262', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 1047], [3, 4, 1745], [5, 6, 2094], [349, 350, 30]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1049804472956300000510713609', 'prec': 100}, 'szpiro_ratio': 3.9034462069263216, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, -1, -1, 1, 1, 1, -4, -1, 1, -1, -4, -1, -2, 4, -1, 1, -6, -1, 4, 1], 'aplist': [-1, -1, 1, -4, -4, -2, -6, 4, 0, 6, 8, -10, 2, 8, -8, 2, 12, -2, 12, -8, 10, 4, 4, 14, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 10470, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '10470.a', 'trace_hash': 1132529548666211445}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.10970493848809066220212642261', 'prec': 103}, 'conductor': 10470, 'gens': [[107, 1239, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.1839591098003210657698858262', 'prec': 100}], 'lmfdb_label': '10470.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.50480603092783358241072724838', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1120877917826519394426941692036178356', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-14, 7, 1]], 'xcoord_integral_points': [-14, 107]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [1, 0], '5': [2, 0], '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '349': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '10470.a4'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 541457
    {'degree': 2, 'field': [-87, -1, 1], 'lmfdb_label': '10470.a4', 'torsion': [4]}
  • id: 541458
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '10470.a4', 'torsion': [4]}
  • id: 541456
    {'degree': 2, 'field': [262, -1, 1], 'lmfdb_label': '10470.a4', 'torsion': [2, 2]}
  • id: 541460
    {'degree': 4, 'field': [2109, 807, 44, -1, 1], 'lmfdb_label': '10470.a4', 'torsion': [8]}
  • id: 541459
    {'degree': 4, 'field': [7569, 87, 88, -1, 1], 'lmfdb_label': '10470.a4', 'torsion': [2, 4]}
  • id: 541464
    {'degree': 8, 'field': [-768, 0, 163, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '10470.a4', 'torsion': [6]}
  • id: 541462
    {'degree': 8, 'field': [2819041, -23506, -234331, -3382, 8248, 154, -139, -2, 1], 'lmfdb_label': '10470.a4', 'torsion': [8]}
  • id: 541463
    {'degree': 8, 'field': [4447881, 1701963, 558453, 39726, 634, -1658, -43, -1, 1], 'lmfdb_label': '10470.a4', 'torsion': [2, 8]}
  • id: 541461
    {'degree': 8, 'field': [50399200, 18135800, 2158625, 237200, 36154, 2356, 350, -2, 1], 'lmfdb_label': '10470.a4', 'torsion': [2, 4]}
  • id: 541470
    {'degree': 16, 'field': [589824, 0, 125184, 0, -47159, 0, 15648, 0, 9984, 0, 326, 0, 96, 0, 0, 0, 1], 'lmfdb_label': '10470.a4', 'torsion': [12]}
  • id: 541469
    {'degree': 16, 'field': [5039864064, 0, 2444108688, 0, 131290425, 0, -2516904, 0, -1128720, 0, -38186, 0, -1272, 0, 0, 0, 1], 'lmfdb_label': '10470.a4', 'torsion': [12]}
  • id: 541466
    {'degree': 16, 'field': [8540717056, 0, 2149965824, 0, -550866176, 0, 311692256, 0, 144178609, 0, -2398111, 0, 27784, 0, -199, 0, 1], 'lmfdb_label': '10470.a4', 'torsion': [2, 8]}
  • id: 541468
    {'degree': 16, 'field': [10212166139904, 0, -742337197056, 0, 44360296000, 0, -1072542528, 0, 36982080, 0, 37547, 0, -9648, 0, 0, 0, 1], 'lmfdb_label': '10470.a4', 'torsion': [2, 6]}
  • id: 541467
    {'degree': 16, 'field': [326807075614400, 367179019782400, -131435781478240, 19001091492160, 3104470832192, -692998778400, 28235579704, 2789195184, -784820672, -84429080, 13748966, 311908, -106879, 3166, 235, -6, 1], 'lmfdb_label': '10470.a4', 'torsion': [16]}
  • id: 541465
    {'degree': 16, 'field': [1833889494532096, -560479674368, 85647872, -2241404836416, 560436771908, -770542924, 1369947154, -513677838, 128602693, -301026, 209416, -78542, 13103, -12, 8, -4, 1], 'lmfdb_label': '10470.a4', 'torsion': [4, 4]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 222229
    {'conductor': 10470, 'conductor_valuation': 1, 'discriminant_valuation': 24, 'j_denominator_valuation': 24, 'kodaira_symbol': 28, 'lmfdb_label': '10470.a4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 222230
    {'conductor': 10470, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '10470.a4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 222231
    {'conductor': 10470, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '10470.a4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 222232
    {'conductor': 10470, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '10470.a4', 'prime': 349, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1733196
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 8370, 8371], [2800, 3, 2797, 2], [8369, 8, 8368, 9], [3145, 3144, 7342, 3151], [6988, 1, 4583, 6], [1051, 1050, 3154, 7339]], 'adelic_image': '8376.48.0.?', 'conductor': 10470, 'lmfdb_label': '10470.a4', 'prime': 0}
  • id: 50375
    {'conductor': 10470, 'elladic_image': '8.12.0.6', 'lmfdb_label': '10470.a4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 445731
    {'lmfdb_iso': '10470.a', 'p': 7, 'prec': 20, 'unit': 1169863496950125, 'val': 2}
  • id: 445729
    {'lmfdb_iso': '10470.a', 'p': 11, 'prec': 20, 'unit': 50301626292718585753, 'val': 1}
  • id: 445735
    {'lmfdb_iso': '10470.a', 'p': 13, 'prec': 20, 'unit': 335758647635726518344, 'val': 1}
  • id: 445737
    {'lmfdb_iso': '10470.a', 'p': 17, 'prec': 20, 'unit': 158026333842089718489403, 'val': 1}
  • id: 445738
    {'lmfdb_iso': '10470.a', 'p': 19, 'prec': 20, 'unit': 1802357894647590115667982, 'val': 1}
  • id: 445734
    {'lmfdb_iso': '10470.a', 'p': 29, 'prec': 20, 'unit': 3292427077657937236601472116, 'val': 1}
  • id: 445747
    {'lmfdb_iso': '10470.a', 'p': 31, 'prec': 20, 'unit': 10645749891182197054477834834, 'val': 1}
  • id: 445730
    {'lmfdb_iso': '10470.a', 'p': 37, 'prec': 20, 'unit': 211788672463256799996047163869, 'val': 1}
  • id: 445732
    {'lmfdb_iso': '10470.a', 'p': 41, 'prec': 20, 'unit': 1787787128731117585391485034786, 'val': 1}
  • id: 445733
    {'lmfdb_iso': '10470.a', 'p': 43, 'prec': 20, 'unit': 5596234277648729819929179625847, 'val': 1}
  • id: 445745
    {'lmfdb_iso': '10470.a', 'p': 47, 'prec': 20, 'unit': 48241620456386659179559852517468, 'val': 1}
  • id: 445739
    {'lmfdb_iso': '10470.a', 'p': 53, 'prec': 20, 'unit': 466280505257343243388047807369661, 'val': 1}
  • id: 445740
    {'lmfdb_iso': '10470.a', 'p': 59, 'prec': 20, 'unit': 4120496079706018406856196308673565, 'val': 1}
  • id: 445746
    {'lmfdb_iso': '10470.a', 'p': 61, 'prec': 20, 'unit': 6736890881523268923570698698574675, 'val': 1}
  • id: 445728
    {'lmfdb_iso': '10470.a', 'p': 67, 'prec': 20, 'unit': 36182118545226121218432256742146238, 'val': 1}
  • id: 445744
    {'lmfdb_iso': '10470.a', 'p': 71, 'prec': 20, 'unit': 139748700205482275557239106727806008, 'val': 1}
  • id: 445741
    {'lmfdb_iso': '10470.a', 'p': 73, 'prec': 20, 'unit': 221332800589175998108352089013958930, 'val': 1}
  • id: 445736
    {'lmfdb_iso': '10470.a', 'p': 79, 'prec': 20, 'unit': 937740454205005162820954314886355563, 'val': 1}
  • id: 445742
    {'lmfdb_iso': '10470.a', 'p': 83, 'prec': 20, 'unit': 2212025673132327895945391935667807276, 'val': 1}
  • id: 445743
    {'lmfdb_iso': '10470.a', 'p': 89, 'prec': 20, 'unit': 4495161552524742526571115080604631614, 'val': 1}
  • id: 445727
    {'lmfdb_iso': '10470.a', 'p': 97, 'prec': 20, 'unit': 45365118913221573851890733918352141902, 'val': 1}