Elliptic curve data - 3136.o2

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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': '3136r', 'Clabel': '3136r3', 'Cnumber': 3, 'abc_quality': 0.9802957926219806, 'absD': 10578455953408, 'ainvs': [0, 0, 0, -6860, -268912], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 14, 'class_size': 4, 'cm': -7, 'conductor': 3136, 'degree': 3584, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2135374563119521995542128442', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 7, 'intrinsic_torsion': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [-3375, 1], 'lmfdb_iso': '3136.o', 'lmfdb_label': '3136.o2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -2, -1], 'min_quad_twist_disc': 56, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.5431194805405979201052828177', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 7], [7, 20, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2856159263194507434006498956', 'prec': 103}, 'szpiro_ratio': 4.785597313312586, '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, 0, 0, 0, 0, 0, 0, 0, -3, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, 0, 0, 4, 0, 0, 0, -8, -2, 0, 6, 0, -12, 0, 10, 0, 0, 4, -16, 0, -8, 0, 0, 0], 'class_deg': 14, 'class_size': 4, 'conductor': 3136, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '3136.o', 'trace_hash': 1660653100846677507}
• 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': '0.088294725005045477437467803003', 'prec': 107}, 'conductor': 3136, 'gens': [[5506, 408512, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '6.5431194805405979201052828177', 'prec': 100}], 'lmfdb_label': '3136.o2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25834964372348823392193774251', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3808251732757577539645724304354720843', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[98, 0, 1]], 'xcoord_integral_points': [98, 5506]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [1, 1, 0], '7': 'a', '11': [1, 0], '13': [1, 1, 0], '17': [1, 3, 0], '19': [1, 3, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '3136.o2'}
• ec_torsion_growth •

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

  
  
  • id: 162602
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '3136.o2', 'torsion': [2, 2]}
  • id: 162603
    {'degree': 4, 'field': [-7, 0, 0, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [4]}
  • id: 162604
    {'degree': 4, 'field': [28, 0, 0, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [2, 4]}
  • id: 162605
    {'degree': 6, 'field': [8, 0, 24, 0, 10, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [14]}
  • id: 162608
    {'degree': 8, 'field': [-2352, 0, -1176, 0, -168, 0, 0, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [6]}
  • id: 162606
    {'degree': 8, 'field': [36, 0, 88, 0, -8, 0, 4, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [4, 4]}
  • id: 162607
    {'degree': 8, 'field': [46, -32, 37, -12, 12, -10, 8, -4, 1], 'lmfdb_label': '3136.o2', 'torsion': [2, 8]}
  • id: 162609
    {'degree': 12, 'field': [64, 0, -32, 0, 16, 0, -8, 0, 4, 0, -2, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [2, 14]}
  • id: 162610
    {'degree': 16, 'field': [1, -4, -26, 8, 83, -104, -40, 108, -56, -80, -10, 12, 3, -4, -4, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [8]}
  • id: 162611
    {'degree': 16, 'field': [256, 0, 0, 0, 25, 0, 0, 0, 19, 0, 0, 0, -5, 0, 0, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [4, 8]}
  • id: 162612
    {'degree': 16, 'field': [1486, 3280, 3676, 1764, -839, -72, 1050, -282, -535, 252, 103, -116, 5, 24, -7, -2, 1], 'lmfdb_label': '3136.o2', 'torsion': [2, 16]}
  • id: 162613
    {'degree': 16, 'field': [5531904, 0, -2765952, 0, 987840, 0, -197568, 0, 30576, 0, -2352, 0, 168, 0, 0, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [6, 6]}
  • id: 162614
    {'degree': 20, 'field': [189314048, 0, 0, 0, 13522432, 0, 0, 0, 241472, 0, 21952, 0, 6272, 0, -784, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3136.o2', 'torsion': [2, 22]}
• 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: 56308
    {'conductor': 3136, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '3136.o2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 56309
    {'conductor': 3136, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '3136.o2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 3136.o2 does not appear in ec_galrep
• ec_padic •

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

  
  
  • id: 102354
    {'lmfdb_iso': '3136.o', 'p': 11, 'prec': 20, 'unit': 31602472903163830446, 'val': 1}
  • id: 102356
    {'lmfdb_iso': '3136.o', 'p': 23, 'prec': 20, 'unit': 53298179011312952408232465, 'val': 1}
  • id: 102357
    {'lmfdb_iso': '3136.o', 'p': 29, 'prec': 20, 'unit': 1080238459007578430922915247, 'val': 1}
  • id: 102350
    {'lmfdb_iso': '3136.o', 'p': 37, 'prec': 20, 'unit': 117511924917053852092521698075, 'val': 1}
  • id: 102352
    {'lmfdb_iso': '3136.o', 'p': 43, 'prec': 20, 'unit': 9566749860576847791181942647914, 'val': 1}
  • id: 102355
    {'lmfdb_iso': '3136.o', 'p': 53, 'prec': 20, 'unit': 463692051158464084073591351624852, 'val': 1}
  • id: 102349
    {'lmfdb_iso': '3136.o', 'p': 67, 'prec': 20, 'unit': 43336574846886154920861252453875154, 'val': 1}
  • id: 102351
    {'lmfdb_iso': '3136.o', 'p': 71, 'prec': 20, 'unit': 35960148510335650793088825683745030, 'val': 1}
  • id: 102353
    {'lmfdb_iso': '3136.o', 'p': 79, 'prec': 20, 'unit': 599335141469597664493344791789343265, 'val': 1}