Elliptic curve data - 2072.d1

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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': '2072b', 'Clabel': '2072b1', 'Cnumber': 1, 'abc_quality': 0.7561763452245515, 'absD': 66304, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 518, 'ainvs': [0, 0, 0, 4, -12], 'analytic_rank': 1, 'bad_primes': [2, 7, 37], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 2072, 'degree': 192, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.39362221043645894405764061308', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1], 'jinv': [27648, 259], 'lmfdb_iso': '2072.d', 'lmfdb_label': '2072.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 4, -12], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['518.2.0.?'], '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': '0.47697563859327156467251239118', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 259], [7, 8, 296], [37, 38, 56]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.85572033080975581700246202739', 'prec': 107}, 'szpiro_ratio': 2.4217268113478068, '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, 0, 0, 0, 3, 0, -1, 0, -3, 0, -3, 0, -5, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 0, 3, -1, -3, -5, 6, 4, -8, -8, -7, -1, 2, -6, 6, 1, -9, 6, -11, -15, 2, -4, 14, -5, 13], 'class_deg': 1, 'class_size': 1, 'conductor': 2072, 'isogeny_matrix': [[1]], 'lmfdb_iso': '2072.d', 'trace_hash': 126272747171335151}
• 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': '2.1973331508093360382144007245', 'prec': 100}, 'conductor': 2072, 'gens': [[2, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.47697563859327156467251239118', 'prec': 103}], 'lmfdb_label': '2072.d1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.7209184298581420346571360289', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2833446681940700641236350398761805834', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [2, 12]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [7, 1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 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': '2072.d1'}
• ec_torsion_growth •

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

  
  
  • id: 105008
    {'degree': 3, 'field': [-12, 4, 0, 1], 'lmfdb_label': '2072.d1', 'torsion': [2]}
  • id: 105009
    {'degree': 6, 'field': [359, -131, 156, -51, 28, -3, 1], 'lmfdb_label': '2072.d1', 'torsion': [2, 2]}
  • id: 105010
    {'degree': 8, 'field': [-432, 0, -1296, 0, 72, 0, 0, 0, 1], 'lmfdb_label': '2072.d1', 'torsion': [3]}
  • id: 105011
    {'degree': 12, 'field': [-2583, -17610, -27592, -9288, 6281, 1020, -2028, -48, 315, -54, -8, 0, 1], 'lmfdb_label': '2072.d1', '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: 34182
    {'conductor': 2072, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '2072.d1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 34183
    {'conductor': 2072, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2072.d1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 34184
    {'conductor': 2072, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2072.d1', 'prime': 37, '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': [[517, 2, 516, 3], [1, 1, 517, 0], [297, 2, 297, 3], [113, 2, 113, 3], [1, 0, 2, 1], [1, 2, 0, 1]], 'adelic_image': '518.2.0.?', 'conductor': 2072, 'lmfdb_label': '2072.d1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 60831
    {'lmfdb_iso': '2072.d', 'p': 5, 'prec': 20, 'unit': 10143530685712, 'val': 1}
  • id: 60830
    {'lmfdb_iso': '2072.d', 'p': 11, 'prec': 20, 'unit': 51080344462507398206, 'val': 1}
  • id: 60836
    {'lmfdb_iso': '2072.d', 'p': 13, 'prec': 20, 'unit': 985351800121571246996, 'val': 1}
  • id: 60838
    {'lmfdb_iso': '2072.d', 'p': 17, 'prec': 20, 'unit': 15452475853401762876943, 'val': 1}
  • id: 60839
    {'lmfdb_iso': '2072.d', 'p': 19, 'prec': 20, 'unit': 1297773182461270632546410, 'val': 1}
  • id: 60843
    {'lmfdb_iso': '2072.d', 'p': 23, 'prec': 20, 'unit': 74482385109008620982378720, 'val': 1}
  • id: 60835
    {'lmfdb_iso': '2072.d', 'p': 29, 'prec': 20, 'unit': 2960501965298828445400422110, 'val': 1}
  • id: 60848
    {'lmfdb_iso': '2072.d', 'p': 31, 'prec': 20, 'unit': 13713296150304597070301665204, 'val': 1}
  • id: 60833
    {'lmfdb_iso': '2072.d', 'p': 41, 'prec': 20, 'unit': 1683383131717892529944537699014, 'val': 1}
  • id: 60834
    {'lmfdb_iso': '2072.d', 'p': 43, 'prec': 20, 'unit': 3221353264033950210482479795188, 'val': 1}
  • id: 60845
    {'lmfdb_iso': '2072.d', 'p': 47, 'prec': 20, 'unit': 53549621017592974041493051503014, 'val': 1}
  • id: 60840
    {'lmfdb_iso': '2072.d', 'p': 53, 'prec': 20, 'unit': 23800278840237865435107420804453862, 'val': -1}
  • id: 60841
    {'lmfdb_iso': '2072.d', 'p': 59, 'prec': 20, 'unit': 743740633487281544721592301491635, 'val': 1}
  • id: 60846
    {'lmfdb_iso': '2072.d', 'p': 61, 'prec': 20, 'unit': 612190428678055888106898597437807, 'val': 1}
  • id: 60829
    {'lmfdb_iso': '2072.d', 'p': 67, 'prec': 20, 'unit': 12604414199460588370260507205664583, 'val': 1}
  • id: 60832
    {'lmfdb_iso': '2072.d', 'p': 71, 'prec': 20, 'unit': 146986024236254495951738939355692202, 'val': 1}
  • id: 60842
    {'lmfdb_iso': '2072.d', 'p': 73, 'prec': 20, 'unit': 10698685262091330009141728639788991, 'val': 1}
  • id: 60837
    {'lmfdb_iso': '2072.d', 'p': 79, 'prec': 20, 'unit': 572262741422992199691051654183302213, 'val': 1}
  • id: 60847
    {'lmfdb_iso': '2072.d', 'p': 83, 'prec': 20, 'unit': 183730959344526054536404439399512879, 'val': 1}
  • id: 60844
    {'lmfdb_iso': '2072.d', 'p': 89, 'prec': 20, 'unit': 6815259985978587945951542376290091587, 'val': 1}
  • id: 60828
    {'lmfdb_iso': '2072.d', 'p': 97, 'prec': 20, 'unit': 26772667588342279960329943569219958081, 'val': 1}