Elliptic curve data - 285.b1

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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': '285b', 'Clabel': '285b2', 'Cnumber': 2, 'abc_quality': 1.09032431601341, 'absD': 2671875, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1140, 'ainvs': [1, 1, 0, -93, -378], 'analytic_rank': 1, 'bad_primes': [3, 5, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 285, 'degree': 48, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.010339841434137691250798070406', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [90458382169, 2671875], 'lmfdb_iso': '285.b', 'lmfdb_label': '285.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -93, -378], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '60.6.0.c.1', '76.6.0.?', '1140.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.0506918313396191072217212868', 'prec': 97}, 'semistable': True, 'serre_invariants': [[2, 2, 19], [3, 4, 19], [5, 6, 57], [19, 20, 15]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.010339841434137691250798070406', 'prec': 97}, 'szpiro_ratio': 4.463193986184111, '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, -2, -3, 1, -1, -2, 1, -4, -2, 1, -1, 2, 1, -1, 1], 'aplist': [1, -1, -1, -2, -2, -4, 2, -1, -4, 4, 0, 0, 0, -10, 12, -2, 4, 2, -16, 0, -2, -8, -12, 0, -16], 'class_deg': 2, 'class_size': 2, 'conductor': 285, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '285.b', 'trace_hash': 1481482587619896808}
• 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': '0.97953267542031848844364172432', 'prec': 97}, 'conductor': 285, 'gens': [[-6, 6, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0506918313396191072217212868', 'prec': 97}], 'lmfdb_label': '285.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.5380021358662494234644042224', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6159662807375552901305053489823245679', 'prec': 127}, 'tamagawa_product': 4, 'torsion_generators': [[-21, 21, 2]], 'xcoord_integral_points': [-6, 26]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [1, 0], '5': [1, 0], '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '285.b1'}
• ec_torsion_growth •

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

  
  
  • id: 11854
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '285.b1', 'torsion': [2, 2]}
  • id: 11855
    {'degree': 4, 'field': [19, 0, -4, 0, 1], 'lmfdb_label': '285.b1', 'torsion': [4]}
  • id: 11857
    {'degree': 8, 'field': [-927, -2156, -136, 988, 194, -76, -8, -4, 1], 'lmfdb_label': '285.b1', 'torsion': [2, 4]}
  • id: 11858
    {'degree': 8, 'field': [-13, 25, -34, 17, -5, -7, 7, -4, 1], 'lmfdb_label': '285.b1', 'torsion': [6]}
  • id: 11856
    {'degree': 8, 'field': [334, -462, 547, -118, 209, 70, -3, -2, 1], 'lmfdb_label': '285.b1', 'torsion': [2, 4]}
  • id: 11860
    {'degree': 16, 'field': [3258025, 0, -5754701, 0, 2649379, 0, -669294, 0, 98553, 0, -10431, 0, 703, 0, -38, 0, 1], 'lmfdb_label': '285.b1', 'torsion': [2, 6]}
  • id: 11859
    {'degree': 16, 'field': [33362176, 0, 29850368, 0, 10038688, 0, 843296, 0, -57095, 0, -1729, 0, 1198, 0, -67, 0, 1], 'lmfdb_label': '285.b1', 'torsion': [8]}
• 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: 2568
    {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '285.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2569
    {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '285.b1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2570
    {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '285.b1', 'prime': 19, '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: 1666938
    {'adelic_gens': [[1, 2, 2, 5], [856, 289, 285, 856], [1, 4, 0, 1], [457, 4, 914, 9], [1137, 4, 1136, 5], [422, 1, 359, 0], [1, 0, 4, 1], [3, 4, 8, 11], [761, 4, 382, 9]], 'adelic_image': '1140.12.0.?', 'conductor': 285, 'lmfdb_label': '285.b1', 'prime': 0}
  • id: 1157
    {'conductor': 285, 'elladic_image': '2.3.0.1', 'lmfdb_label': '285.b1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2868
    {'lmfdb_iso': '285.b', 'p': 7, 'prec': 20, 'unit': 814501440543683, 'val': 2}
  • id: 2867
    {'lmfdb_iso': '285.b', 'p': 11, 'prec': 20, 'unit': 55570126955251739125, 'val': 1}
  • id: 2872
    {'lmfdb_iso': '285.b', 'p': 13, 'prec': 20, 'unit': 352547054973044208513, 'val': 1}
  • id: 2874
    {'lmfdb_iso': '285.b', 'p': 17, 'prec': 20, 'unit': 208637164564806833937480, 'val': 1}
  • id: 2878
    {'lmfdb_iso': '285.b', 'p': 23, 'prec': 20, 'unit': 19239052654045384991650013, 'val': 1}
  • id: 2871
    {'lmfdb_iso': '285.b', 'p': 29, 'prec': 20, 'unit': 5850240055210697281781962630, 'val': 1}
  • id: 2870
    {'lmfdb_iso': '285.b', 'p': 43, 'prec': 20, 'unit': 2559769960600588066568822461892, 'val': 1}
  • id: 2879
    {'lmfdb_iso': '285.b', 'p': 47, 'prec': 20, 'unit': 35994852259552645175441521338179, 'val': 1}
  • id: 2876
    {'lmfdb_iso': '285.b', 'p': 53, 'prec': 20, 'unit': 493415569975492065533368733341069, 'val': 1}
  • id: 2877
    {'lmfdb_iso': '285.b', 'p': 59, 'prec': 20, 'unit': 3521156092244584619628825582253656, 'val': 1}
  • id: 2880
    {'lmfdb_iso': '285.b', 'p': 61, 'prec': 20, 'unit': 1578398457465121233334040568273775, 'val': 1}
  • id: 2875
    {'lmfdb_iso': '285.b', 'p': 67, 'prec': 20, 'unit': 29613521996341528235852970552185832, 'val': 1}
  • id: 2869
    {'lmfdb_iso': '285.b', 'p': 73, 'prec': 20, 'unit': 155287867585464610386784103081423056, 'val': 1}
  • id: 2873
    {'lmfdb_iso': '285.b', 'p': 79, 'prec': 20, 'unit': 323438519674355648512520777027062632, 'val': 1}
  • id: 2866
    {'lmfdb_iso': '285.b', 'p': 83, 'prec': 20, 'unit': 71119689953115736601831503840112771, 'val': 1}
  • id: 2865
    {'lmfdb_iso': '285.b', 'p': 97, 'prec': 20, 'unit': 22941949154130126226723588028343388840, 'val': 1}