Elliptic curve data - 15075.a1

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

  
  {'Ciso': '15075k', 'Clabel': '15075k1', 'Cnumber': 1, 'abc_quality': 0.800359374985248, 'absD': 6868546875, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 134, 'ainvs': [0, 0, 1, 375, -2844], 'analytic_rank': 1, 'bad_primes': [3, 5, 67], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 15075, 'degree': 13824, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.57379147081596012824428907054', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [512000, 603], 'lmfdb_iso': '15075.a', 'lmfdb_label': '15075.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, 2, 0], 'min_quad_twist_disc': -15, 'modell_images': [], 'modm_images': ['134.2.0.?'], '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': '0.79731429162447596496177777243', 'prec': 103}, 'semistable': False, 'serre_invariants': [[3, 8, 1675], [5, 14, 603], [67, 68, 225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.78023362973514490475371321453', 'prec': 107}, 'szpiro_ratio': 3.058885399254388, '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, -2, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, -4, 0, 0, -4, -7, 0, -5, 0], 'aplist': [-2, 0, 0, 0, 6, -4, -7, -5, -1, -1, -4, -3, 0, 6, 9, 10, -3, 2, 1, 16, 7, 8, -4, 15, -4], 'class_deg': 1, 'class_size': 1, 'conductor': 15075, 'isogeny_matrix': [[1]], 'lmfdb_iso': '15075.a', 'trace_hash': 1725787913759616297}
• 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': '0.31740302460087110803483262175', 'prec': 103}, 'conductor': 15075, 'gens': [[20, 112, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.79731429162447596496177777243', 'prec': 103}], 'lmfdb_label': '15075.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.71477326573909523724364674002', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2795957601795201396627908194068429957', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [9, 20]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 5, 0], '3': 'a', '5': 'a', '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [3, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0], '67': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '15075.a1'}
• ec_torsion_growth •

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

  
  
  • id: 775395
    {'degree': 3, 'field': [5, -3, -1, 1], 'lmfdb_label': '15075.a1', 'torsion': [2]}
  • id: 775396
    {'degree': 6, 'field': [9, -27, 34, -23, 8, -1, 1], 'lmfdb_label': '15075.a1', 'torsion': [2, 2]}
  • id: 775397
    {'degree': 8, 'field': [-6929, -4111, 3802, 617, -305, -7, 7, -4, 1], 'lmfdb_label': '15075.a1', 'torsion': [3]}
  • id: 775398
    {'degree': 12, 'field': [616861, 701330, -32800, -309942, -132909, -13196, 5888, 3124, 695, -110, 0, -6, 1], 'lmfdb_label': '15075.a1', '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: 333031
    {'conductor': 15075, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '15075.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 333032
    {'conductor': 15075, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '15075.a1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 333033
    {'conductor': 15075, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15075.a1', 'prime': 67, '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': [[1, 2, 0, 1], [1, 0, 2, 1], [1, 1, 133, 0], [133, 2, 132, 3], [69, 2, 69, 3]], 'adelic_image': '134.2.0.?', 'conductor': 15075, 'lmfdb_label': '15075.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 676613
    {'lmfdb_iso': '15075.a', 'p': 11, 'prec': 20, 'unit': 54560685735520151057, 'val': 1}
  • id: 676619
    {'lmfdb_iso': '15075.a', 'p': 13, 'prec': 20, 'unit': 601153605250134869396, 'val': 1}
  • id: 676621
    {'lmfdb_iso': '15075.a', 'p': 17, 'prec': 20, 'unit': 107132699532145533096115, 'val': 1}
  • id: 676622
    {'lmfdb_iso': '15075.a', 'p': 19, 'prec': 20, 'unit': 866780122437626501008685, 'val': 1}
  • id: 676625
    {'lmfdb_iso': '15075.a', 'p': 23, 'prec': 20, 'unit': 53743478938075495712699284, 'val': 1}
  • id: 676618
    {'lmfdb_iso': '15075.a', 'p': 29, 'prec': 20, 'unit': 975587205322322013597026740, 'val': 1}
  • id: 676629
    {'lmfdb_iso': '15075.a', 'p': 31, 'prec': 20, 'unit': 16683553548290641492805463915, 'val': 1}
  • id: 676614
    {'lmfdb_iso': '15075.a', 'p': 37, 'prec': 20, 'unit': 11076217940950514223449014945, 'val': 2}
  • id: 676617
    {'lmfdb_iso': '15075.a', 'p': 43, 'prec': 20, 'unit': 8863994062624017975110992965748, 'val': 1}
  • id: 676627
    {'lmfdb_iso': '15075.a', 'p': 47, 'prec': 20, 'unit': 48318055201045187739597089796197, 'val': 1}
  • id: 676623
    {'lmfdb_iso': '15075.a', 'p': 53, 'prec': 20, 'unit': 101451352434445824952582517637750, 'val': 1}
  • id: 676624
    {'lmfdb_iso': '15075.a', 'p': 59, 'prec': 20, 'unit': 11323732572069405235945310813740, 'val': 1}
  • id: 676628
    {'lmfdb_iso': '15075.a', 'p': 61, 'prec': 20, 'unit': 2045780347036012229504691137037745, 'val': 1}
  • id: 676615
    {'lmfdb_iso': '15075.a', 'p': 71, 'prec': 20, 'unit': 104824890945103722435954866391647660, 'val': 1}
  • id: 676616
    {'lmfdb_iso': '15075.a', 'p': 73, 'prec': 20, 'unit': 139464797834550480169780192213954399, 'val': 1}
  • id: 676620
    {'lmfdb_iso': '15075.a', 'p': 79, 'prec': 20, 'unit': 334643067718058304233830252720081557, 'val': 1}
  • id: 676612
    {'lmfdb_iso': '15075.a', 'p': 83, 'prec': 20, 'unit': 241210244212741432007407839059308365, 'val': 1}
  • id: 676626
    {'lmfdb_iso': '15075.a', 'p': 89, 'prec': 20, 'unit': 8615836129819964574668126228394018279, 'val': 1}
  • id: 676611
    {'lmfdb_iso': '15075.a', 'p': 97, 'prec': 20, 'unit': 26707058675698214224691501933785831328, 'val': 1}