Elliptic curve data - 4050.r2

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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': '4050g', 'Clabel': '4050g1', 'Cnumber': 1, 'abc_quality': 1.2854862760382055, 'absD': 81000000, 'adelic_genus': 1, 'adelic_index': 128, 'adelic_level': 60, 'ainvs': [1, -1, 0, 108, 16], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 4050, 'degree': 1296, 'elladic_images': ['4.8.0.2', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.20691247027446084460658893445', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 3], 'jinv': [109503, 64], 'lmfdb_iso': '4050.r', 'lmfdb_label': '4050.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 39, -19], 'min_quad_twist_disc': -15, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '4.8.0.b.1', '12.64.1.b.1', '15.8.0-3.a.1.2', '20.16.0-4.b.1.1', '60.128.1-12.b.1.3'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3087114658062606465607446284', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2025], [3, 8, 25], [5, 14, 162]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.96401058216529257315887247780', 'prec': 107}, 'szpiro_ratio': 3.088529445464373, '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, 0, 0, 4, -1, 0, 0, 0, 0, 1, -4, 0, 1, -3, 0, -4, 0], 'aplist': [-1, 0, 0, 4, 0, 1, -3, -4, 0, -9, -4, 1, -6, -8, -12, -6, 0, -1, 4, 12, -11, -16, -12, 3, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 4050, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '4050.r', 'trace_hash': 1933196064960801250}
• 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': '0.66111667585864960697726436723', 'prec': 103}, 'conductor': 4050, 'gens': [[0, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3087114658062606465607446284', 'prec': 100}], 'lmfdb_label': '4050.r2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.1650675545777461209753544721', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0494745342295154044410451955697941984', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [0, 183]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 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]}, 'iwp0': 0, 'lmfdb_label': '4050.r2'}
• ec_torsion_growth •

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

  
  
  • id: 211736
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '4050.r2', 'torsion': [3]}
  • id: 211737
    {'degree': 3, 'field': [-4, -3, 0, 1], 'lmfdb_label': '4050.r2', 'torsion': [2]}
  • id: 211739
    {'degree': 6, 'field': [-16, 12, 9, -16, -9, 0, 1], 'lmfdb_label': '4050.r2', 'torsion': [12]}
  • id: 211738
    {'degree': 6, 'field': [2, 6, 9, -2, 0, 0, 1], 'lmfdb_label': '4050.r2', 'torsion': [2, 2]}
  • id: 211740
    {'degree': 6, 'field': [9, 18, 54, -4, 6, 0, 1], 'lmfdb_label': '4050.r2', 'torsion': [4]}
  • id: 211741
    {'degree': 6, 'field': [24, 0, 0, -9, 0, 0, 1], 'lmfdb_label': '4050.r2', 'torsion': [3]}
  • id: 211742
    {'degree': 12, 'field': [4, -12, 18, 70, 117, 18, 32, 66, 63, -8, 0, 0, 1], 'lmfdb_label': '4050.r2', 'torsion': [4, 12]}
  • id: 211743
    {'degree': 12, 'field': [9, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '4050.r2', 'torsion': [3, 3]}
  • id: 211744
    {'degree': 18, 'field': [-16, 0, 0, 432, 0, -1188, 729, 1044, -2187, -304, 2430, 0, -1215, 0, 270, 0, -27, 0, 1], 'lmfdb_label': '4050.r2', 'torsion': [9]}
  • id: 211745
    {'degree': 18, 'field': [4096, 0, 0, -11640, 0, 0, 9132, 0, 0, -1123, 0, 0, 141, 0, 0, -3, 0, 0, 1], 'lmfdb_label': '4050.r2', 'torsion': [6]}
• 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: 75958
    {'conductor': 4050, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '4050.r2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 75959
    {'conductor': 4050, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '4050.r2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 75960
    {'conductor': 4050, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4050.r2', 'prime': 5, 'reduction_type': 0, '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: 1690398
    {'adelic_gens': [[21, 40, 40, 21], [25, 36, 24, 25], [1, 0, 36, 1], [23, 0, 0, 59], [1, 45, 45, 46], [31, 15, 0, 1], [21, 40, 20, 41]], 'adelic_image': '60.128.1.?', 'conductor': 4050, 'lmfdb_label': '4050.r2', 'prime': 0}
  • id: 20232
    {'conductor': 4050, 'elladic_image': '4.8.0.2', 'lmfdb_label': '4050.r2', 'modell_image': '2G', 'prime': 2}
  • id: 20233
    {'conductor': 4050, 'elladic_image': '3.4.0.1', 'lmfdb_label': '4050.r2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 142086
    {'lmfdb_iso': '4050.r', 'p': 7, 'prec': 20, 'unit': 91873098462505, 'val': 1}
  • id: 142090
    {'lmfdb_iso': '4050.r', 'p': 13, 'prec': 20, 'unit': 18612709847264045326296, 'val': -1}
  • id: 142092
    {'lmfdb_iso': '4050.r', 'p': 17, 'prec': 20, 'unit': 63043501295235828669175, 'val': 1}
  • id: 142093
    {'lmfdb_iso': '4050.r', 'p': 19, 'prec': 20, 'unit': 618337028258813203992224, 'val': 1}
  • id: 142089
    {'lmfdb_iso': '4050.r', 'p': 29, 'prec': 20, 'unit': 3705378297852746398864945882, 'val': 1}
  • id: 142100
    {'lmfdb_iso': '4050.r', 'p': 31, 'prec': 20, 'unit': 16826917551619355096791111158, 'val': 1}
  • id: 142085
    {'lmfdb_iso': '4050.r', 'p': 37, 'prec': 20, 'unit': 1550055272781659878403574712108, 'val': -1}
  • id: 142087
    {'lmfdb_iso': '4050.r', 'p': 41, 'prec': 20, 'unit': 1852567689768577908351280528528, 'val': 1}
  • id: 142088
    {'lmfdb_iso': '4050.r', 'p': 43, 'prec': 20, 'unit': 5334739401202403300082920605452, 'val': 1}
  • id: 142091
    {'lmfdb_iso': '4050.r', 'p': 47, 'prec': 20, 'unit': 29936271406923317589258950653322, 'val': 1}
  • id: 142094
    {'lmfdb_iso': '4050.r', 'p': 53, 'prec': 20, 'unit': 501737713989756830187705895034729, 'val': 1}
  • id: 142099
    {'lmfdb_iso': '4050.r', 'p': 61, 'prec': 20, 'unit': 6270608135258004284417206275907082, 'val': 1}
  • id: 142084
    {'lmfdb_iso': '4050.r', 'p': 67, 'prec': 20, 'unit': 35587519588895910428402181537600708, 'val': 1}
  • id: 142097
    {'lmfdb_iso': '4050.r', 'p': 71, 'prec': 20, 'unit': 830351678475231041946531103846133, 'val': 1}
  • id: 142095
    {'lmfdb_iso': '4050.r', 'p': 73, 'prec': 20, 'unit': 240821136952693355066040153954876718, 'val': 1}
  • id: 142098
    {'lmfdb_iso': '4050.r', 'p': 79, 'prec': 20, 'unit': 123121050467811385215806516744714184, 'val': 1}
  • id: 142083
    {'lmfdb_iso': '4050.r', 'p': 83, 'prec': 20, 'unit': 24287027828360220937810075879567068, 'val': 2}
  • id: 142096
    {'lmfdb_iso': '4050.r', 'p': 89, 'prec': 20, 'unit': 9307812117359732462102978398210546959, 'val': 1}
  • id: 142082
    {'lmfdb_iso': '4050.r', 'p': 97, 'prec': 20, 'unit': 25157863059547848257915474199220356656, 'val': 1}