Elliptic curve data - 104742.w1

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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': '104742h', 'Clabel': '104742h1', 'Cnumber': 1, 'abc_quality': 0.9694771563045855, 'absD': 1244428703671032, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 6072, 'ainvs': [1, -1, 0, 20394, -1279476], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 23], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 104742, 'degree': 539136, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5822818312371411722866938759', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 22, 'isogeny_degrees': [1], 'jinv': [105756712489, 140300424], 'lmfdb_iso': '104742.w', 'lmfdb_label': '104742.w1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 2266, 47388], 'min_quad_twist_disc': -3, 'modell_images': [], 'modm_images': ['6072.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.1453861587185778212486231621', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2277], [3, 8, 5819], [11, 12, 9522], [23, 156, 198]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.24910213292079890388738304949', 'prec': 103}, 'szpiro_ratio': 3.602228749563905, '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, 2, 0, -1, -1, 0, -2, -1, 0, 5, 1, 0, 1, 4, 0, 4, 2], 'aplist': [-1, 0, 2, -1, -1, 5, 4, 4, 0, 6, -3, -7, -11, 8, 6, 12, -1, -6, -1, -14, -4, 8, 3, 18, 6], 'class_deg': 1, 'class_size': 1, 'conductor': 104742, 'isogeny_matrix': [[1]], 'lmfdb_iso': '104742.w', 'trace_hash': 699114359131878267}
• 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': '0.042232565447464916149764824404', 'prec': 107}, 'conductor': 104742, 'gens': [[11805, 1276773, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.1453861587185778212486231621', 'prec': 100}], 'lmfdb_label': '104742.w1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25858789577127454860327459902', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.5068703053690338075122134166524496271', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [11805]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [7, 0], '3': 'a', '5': [1, 0], '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': 'a', '29': [3, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '104742.w1'}
• ec_torsion_growth •

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

  
  
  • id: 4844932
    {'degree': 3, 'field': [-30, 22, -1, 1], 'lmfdb_label': '104742.w1', 'torsion': [2]}
  • id: 4844933
    {'degree': 6, 'field': [7368, -5928, 1594, -68, -3, -2, 1], 'lmfdb_label': '104742.w1', 'torsion': [2, 2]}
  • id: 4844934
    {'degree': 8, 'field': [40716, -59694, 45507, -20052, 4896, -756, 72, -2, 1], 'lmfdb_label': '104742.w1', 'torsion': [3]}
  • id: 4844935
    {'degree': 12, 'field': [-9226020, -18289672, -11393177, -3025370, 106385, 235096, 49258, 7740, -510, -528, -1, -2, 1], 'lmfdb_label': '104742.w1', '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: 2573316
    {'conductor': 104742, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '104742.w1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2573317
    {'conductor': 104742, 'conductor_valuation': 2, 'discriminant_valuation': 19, 'j_denominator_valuation': 13, 'kodaira_symbol': -17, 'lmfdb_label': '104742.w1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2573318
    {'conductor': 104742, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '104742.w1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2573319
    {'conductor': 104742, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '104742.w1', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• 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': [[1519, 2, 0, 1], [4049, 2, 4049, 3], [1, 0, 2, 1], [1, 2, 0, 1], [3961, 2, 3961, 3], [6071, 2, 6070, 3], [3313, 2, 3313, 3], [3037, 2, 3037, 3], [1, 1, 6071, 0]], 'adelic_image': '6072.2.0.?', 'conductor': 104742, 'lmfdb_label': '104742.w1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 5455315
    {'lmfdb_iso': '104742.w', 'p': 5, 'prec': 20, 'unit': 3584971294678, 'val': 1}
  • id: 5455316
    {'lmfdb_iso': '104742.w', 'p': 7, 'prec': 20, 'unit': 2992312944442, 'val': 5}
  • id: 5455321
    {'lmfdb_iso': '104742.w', 'p': 13, 'prec': 20, 'unit': 1186804408313860773627, 'val': 1}
  • id: 5455323
    {'lmfdb_iso': '104742.w', 'p': 17, 'prec': 20, 'unit': 180779407987354568597559, 'val': 1}
  • id: 5455324
    {'lmfdb_iso': '104742.w', 'p': 19, 'prec': 20, 'unit': 1471946389296912726549263, 'val': 1}
  • id: 5455320
    {'lmfdb_iso': '104742.w', 'p': 29, 'prec': 20, 'unit': 97040267758434747300857966, 'val': 2}
  • id: 5455317
    {'lmfdb_iso': '104742.w', 'p': 31, 'prec': 20, 'unit': 5851555700868071892709922630, 'val': 1}
  • id: 5455332
    {'lmfdb_iso': '104742.w', 'p': 37, 'prec': 20, 'unit': 279990479899369623191670604198, 'val': 1}
  • id: 5455318
    {'lmfdb_iso': '104742.w', 'p': 41, 'prec': 20, 'unit': 4205681881629330967622354020576, 'val': 1}
  • id: 5455319
    {'lmfdb_iso': '104742.w', 'p': 43, 'prec': 20, 'unit': 5944562988109351390409339303221, 'val': 1}
  • id: 5455330
    {'lmfdb_iso': '104742.w', 'p': 47, 'prec': 20, 'unit': 46583096466362570901830239559953, 'val': 1}
  • id: 5455325
    {'lmfdb_iso': '104742.w', 'p': 53, 'prec': 20, 'unit': 372219609951151144553012715236204, 'val': 1}
  • id: 5455326
    {'lmfdb_iso': '104742.w', 'p': 59, 'prec': 20, 'unit': 4251187769088473456964226126927277, 'val': 1}
  • id: 5455331
    {'lmfdb_iso': '104742.w', 'p': 61, 'prec': 20, 'unit': 4465636676074283111737488189820950, 'val': 1}
  • id: 5455314
    {'lmfdb_iso': '104742.w', 'p': 67, 'prec': 20, 'unit': 32974767819951116051417922427910530, 'val': 1}
  • id: 5455329
    {'lmfdb_iso': '104742.w', 'p': 71, 'prec': 20, 'unit': 66066026858515793222955045527136118, 'val': 1}
  • id: 5455327
    {'lmfdb_iso': '104742.w', 'p': 73, 'prec': 20, 'unit': 52122940831347107403015982520019906, 'val': 1}
  • id: 5455322
    {'lmfdb_iso': '104742.w', 'p': 79, 'prec': 20, 'unit': 184980923265288878097072342552161965, 'val': 1}
  • id: 5455313
    {'lmfdb_iso': '104742.w', 'p': 83, 'prec': 20, 'unit': 1030654622022200451812386854963739800, 'val': 1}
  • id: 5455328
    {'lmfdb_iso': '104742.w', 'p': 89, 'prec': 20, 'unit': 880473206617118045278839835485692491, 'val': 1}
  • id: 5455312
    {'lmfdb_iso': '104742.w', 'p': 97, 'prec': 20, 'unit': 50131624445401259992443184241378245285, 'val': 1}