Elliptic curve data - 49419.f1

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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
  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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '49419g', 'Clabel': '49419g1', 'Cnumber': 1, 'abc_quality': 0.809432895914023, 'absD': 1837349001, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 3876, 'ainvs': [1, -1, 1, -437, 4182], 'analytic_rank': 1, 'bad_primes': [3, 17, 19], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 49419, 'degree': 15360, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.50045398216501818976272955243', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1], 'jinv': [-2571353, 513], 'lmfdb_iso': '49419.f', 'lmfdb_label': '49419.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -48, -171], 'min_quad_twist_disc': -3, 'modell_images': [], 'modm_images': ['3876.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.72444990406113394630668937007', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.75715549818309067599727672050', 'prec': 107}, 'szpiro_ratio': 2.7893421598935326, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, -1, 1, 0, 1, 3, 0, -1, 0, 0, 4, -1, 0, -1, 0, 0, 1, -1], 'aplist': [-1, 0, 1, 1, 0, 4, 0, 1, -4, -6, -8, 2, -8, 2, 7, -3, -6, 8, 7, 9, -4, 4, -5, 9, -3], 'class_deg': 1, 'class_size': 1, 'conductor': 49419, 'isogeny_matrix': [[1]], 'lmfdb_iso': '49419.f', 'trace_hash': 1965288578404039341}
• 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': '0.36754557135498387980491679568', 'prec': 103}, 'conductor': 49419, 'gens': [[-4, 78, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.72444990406113394630668937007', 'prec': 103}], 'lmfdb_label': '49419.f1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.4228480788702331448829114637', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1231286169244365932970890249722828305', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-4, 15]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': 'a', '19': [2, 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': '49419.f1'}
• ec_torsion_growth •

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

  
  
  • id: 2404137
    {'degree': 3, 'field': [-36, -3, 0, 1], 'lmfdb_label': '49419.f1', 'torsion': [2]}
  • id: 2404138
    {'degree': 6, 'field': [5184, 2160, 1050, 114, 31, -2, 1], 'lmfdb_label': '49419.f1', 'torsion': [2, 2]}
  • id: 2404139
    {'degree': 8, 'field': [89, -231, -504, -383, -92, -41, 20, -2, 1], 'lmfdb_label': '49419.f1', 'torsion': [3]}
  • id: 2404140
    {'degree': 12, 'field': [-71690496, 0, -2908496, 0, -17340, 0, -11560, 0, -952, 0, 0, 0, 1], 'lmfdb_label': '49419.f1', 'torsion': [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: 1181962
    {'conductor': 49419, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '49419.f1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1181963
    {'conductor': 49419, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '49419.f1', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1181964
    {'conductor': 49419, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '49419.f1', '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

  
  {'adelic_gens': [[2281, 2, 2281, 3], [3061, 2, 3061, 3], [1, 2, 0, 1], [1, 0, 2, 1], [1, 1, 3875, 0], [1939, 2, 1939, 3], [2585, 2, 2585, 3], [3875, 2, 3874, 3]], 'adelic_image': '3876.2.0.?', 'conductor': 49419, 'lmfdb_label': '49419.f1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2481634
    {'lmfdb_iso': '49419.f', 'p': 5, 'prec': 20, 'unit': 19375232588228, 'val': -1}
  • id: 2481635
    {'lmfdb_iso': '49419.f', 'p': 7, 'prec': 20, 'unit': 49914099167391079, 'val': -1}
  • id: 2481640
    {'lmfdb_iso': '49419.f', 'p': 13, 'prec': 20, 'unit': 184506354236660400050, 'val': 1}
  • id: 2481646
    {'lmfdb_iso': '49419.f', 'p': 23, 'prec': 20, 'unit': 58388699893088636721400434, 'val': 1}
  • id: 2481639
    {'lmfdb_iso': '49419.f', 'p': 29, 'prec': 20, 'unit': 3836884147343358630040533174, 'val': 1}
  • id: 2481636
    {'lmfdb_iso': '49419.f', 'p': 31, 'prec': 20, 'unit': 5313312548284823673647429769, 'val': 1}
  • id: 2481651
    {'lmfdb_iso': '49419.f', 'p': 37, 'prec': 20, 'unit': 239650268727251853541857666027, 'val': 1}
  • id: 2481637
    {'lmfdb_iso': '49419.f', 'p': 41, 'prec': 20, 'unit': 181706852916168838758708244904, 'val': 1}
  • id: 2481638
    {'lmfdb_iso': '49419.f', 'p': 43, 'prec': 20, 'unit': 2551889314979288687870416356827, 'val': 1}
  • id: 2481649
    {'lmfdb_iso': '49419.f', 'p': 47, 'prec': 20, 'unit': 21300825822467243900249887584498, 'val': 1}
  • id: 2481644
    {'lmfdb_iso': '49419.f', 'p': 53, 'prec': 20, 'unit': 162551555077612642037137336934687, 'val': 1}
  • id: 2481642
    {'lmfdb_iso': '49419.f', 'p': 59, 'prec': 20, 'unit': 2789517467053281783422482512554831, 'val': 1}
  • id: 2481650
    {'lmfdb_iso': '49419.f', 'p': 61, 'prec': 20, 'unit': 5165556482829594522663905004841863, 'val': 1}
  • id: 2481633
    {'lmfdb_iso': '49419.f', 'p': 67, 'prec': 20, 'unit': 36955548268123917224012131004383505, 'val': 1}
  • id: 2481648
    {'lmfdb_iso': '49419.f', 'p': 71, 'prec': 20, 'unit': 41770459164077417666989320240192591, 'val': 1}
  • id: 2481645
    {'lmfdb_iso': '49419.f', 'p': 73, 'prec': 20, 'unit': 35209130082237313639999033862334423, 'val': 1}
  • id: 2481641
    {'lmfdb_iso': '49419.f', 'p': 79, 'prec': 20, 'unit': 220602266006614690508167084771517206, 'val': 1}
  • id: 2481643
    {'lmfdb_iso': '49419.f', 'p': 83, 'prec': 20, 'unit': 2379527993866294132518756685519896216, 'val': 1}
  • id: 2481647
    {'lmfdb_iso': '49419.f', 'p': 89, 'prec': 20, 'unit': 5508023534742599654346252995637778488, 'val': 1}
  • id: 2481632
    {'lmfdb_iso': '49419.f', 'p': 97, 'prec': 20, 'unit': 47118448916890877721828497194505935304, 'val': 1}