Elliptic curve data - 47040.fx2

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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': '47040hh', 'Clabel': '47040hh2', 'Cnumber': 2, 'abc_quality': 0.9653881815131621, 'absD': 5312840601600, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 1, 0, -13785, -617625], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 47040, 'degree': 147456, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2365407151917727615394983167', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 153, 'isogeny_degrees': [1, 2], 'jinv': [601211584, 11025], 'lmfdb_iso': '47040.fx', 'lmfdb_label': '47040.fx2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -70, -200], 'min_quad_twist_disc': 56, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '56.24.0-56.a.1.1', '60.24.0-60.a.1.6', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7621033713838368781899372220', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 15680], [5, 6, 9408], [7, 32, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.42956153989582920043041017648', 'prec': 107}, 'szpiro_ratio': 3.7372065673080597, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
• 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, 1, 0, 1, 0, 0, 0, 1, 0, -4, 0, 6, 0, 1, 0, 6, 0, 4, 0], 'aplist': [0, 1, 1, 0, -4, 6, 6, 4, -8, -10, -4, 6, -6, -4, 12, -6, 4, -2, -4, 0, 2, -8, -12, -14, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 47040, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '47040.fx', 'trace_hash': 1537689022206197077}
• 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': '0.084324617810526361317457392959', 'prec': 107}, 'conductor': 47040, 'gens': [[263, 3744, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.7621033713838368781899372220', 'prec': 100}], 'lmfdb_label': '47040.fx2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.44109153883186025496491657289', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.4020940166403452865222616289510476348', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-61, 0, 1], [135, 0, 1]], 'xcoord_integral_points': [-75, -61, 135, 263]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [2, 0], '7': 'a', '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': '47040.fx2'}
• ec_torsion_growth •

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

  
  
  • id: 2297850
    {'degree': 2, 'field': [-210, 0, 1], 'lmfdb_label': '47040.fx2', 'torsion': [2, 4]}
  • id: 2297851
    {'degree': 4, 'field': [49, 0, 0, 0, 1], 'lmfdb_label': '47040.fx2', 'torsion': [2, 4]}
  • id: 2297852
    {'degree': 4, 'field': [841, 0, -2, 0, 1], 'lmfdb_label': '47040.fx2', 'torsion': [2, 4]}
  • id: 2297855
    {'degree': 8, 'field': [-588, 0, 728, 0, 84, 0, 0, 0, 1], 'lmfdb_label': '47040.fx2', 'torsion': [2, 6]}
  • id: 2297854
    {'degree': 8, 'field': [1, 0, -6724, 0, 3366, 0, -4, 0, 1], 'lmfdb_label': '47040.fx2', 'torsion': [2, 8]}
  • id: 2297853
    {'degree': 8, 'field': [3490, 1900, -1706, -404, 243, -52, 22, -4, 1], 'lmfdb_label': '47040.fx2', 'torsion': [4, 4]}
  • id: 2297858
    {'degree': 16, 'field': [9, 0, -161328, 0, -429980, 0, -322656, 0, 30, 0, 53776, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '47040.fx2', 'torsion': [2, 12]}
  • id: 2297856
    {'degree': 16, 'field': [196, -1568, 6272, -15680, 26544, -30688, 23296, -9520, -404, 2960, -1664, 512, 24, -80, 32, -8, 1], 'lmfdb_label': '47040.fx2', 'torsion': [2, 8]}
  • id: 2297857
    {'degree': 16, 'field': [229441, 0, 846748, 0, 804568, 0, 257236, 0, 49390, 0, 1876, 0, 88, 0, 28, 0, 1], 'lmfdb_label': '47040.fx2', 'torsion': [2, 8]}
• 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: 1123790
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '47040.fx2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1123791
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '47040.fx2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1123792
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '47040.fx2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1123793
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '47040.fx2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1977633
    {'adelic_gens': [[837, 4, 836, 5], [599, 836, 358, 831], [627, 838, 8, 5], [419, 836, 838, 831], [1, 4, 0, 1], [281, 2, 0, 1], [1, 0, 4, 1], [337, 2, 0, 1]], 'adelic_image': '840.48.0.?', 'conductor': 47040, 'lmfdb_label': '47040.fx2', 'prime': 0}
  • id: 203569
    {'conductor': 47040, 'elladic_image': '4.12.0.1', 'lmfdb_label': '47040.fx2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2359752
    {'lmfdb_iso': '47040.fx', 'p': 11, 'prec': 20, 'unit': 29075447983149053071, 'val': 1}
  • id: 2359757
    {'lmfdb_iso': '47040.fx', 'p': 13, 'prec': 20, 'unit': 1126356609860626607491, 'val': 1}
  • id: 2359759
    {'lmfdb_iso': '47040.fx', 'p': 17, 'prec': 20, 'unit': 170664345015882888697895, 'val': 1}
  • id: 2359760
    {'lmfdb_iso': '47040.fx', 'p': 19, 'prec': 20, 'unit': 166604044757078785488770, 'val': 1}
  • id: 2359764
    {'lmfdb_iso': '47040.fx', 'p': 23, 'prec': 20, 'unit': 33195341555541840633380061, 'val': 1}
  • id: 2359756
    {'lmfdb_iso': '47040.fx', 'p': 29, 'prec': 20, 'unit': 5588047159387937158075296269, 'val': 1}
  • id: 2359769
    {'lmfdb_iso': '47040.fx', 'p': 31, 'prec': 20, 'unit': 6946205335056076543571168332, 'val': 1}
  • id: 2359753
    {'lmfdb_iso': '47040.fx', 'p': 37, 'prec': 20, 'unit': 578252913438236820441891325579, 'val': 1}
  • id: 2359754
    {'lmfdb_iso': '47040.fx', 'p': 41, 'prec': 20, 'unit': 3428863668725484218780091517131, 'val': 1}
  • id: 2359755
    {'lmfdb_iso': '47040.fx', 'p': 43, 'prec': 20, 'unit': 1216594854299580705682838629693, 'val': 1}
  • id: 2359766
    {'lmfdb_iso': '47040.fx', 'p': 47, 'prec': 20, 'unit': 16643425452679820571771586804277, 'val': 1}
  • id: 2359761
    {'lmfdb_iso': '47040.fx', 'p': 53, 'prec': 20, 'unit': 365018323402014846537391960166555, 'val': 1}
  • id: 2359762
    {'lmfdb_iso': '47040.fx', 'p': 59, 'prec': 20, 'unit': 3156327789856165688417528083081539, 'val': 1}
  • id: 2359767
    {'lmfdb_iso': '47040.fx', 'p': 61, 'prec': 20, 'unit': 4761334982303984806851193472539712, 'val': 1}
  • id: 2359751
    {'lmfdb_iso': '47040.fx', 'p': 67, 'prec': 20, 'unit': 42804230934494214705549355060170223, 'val': 1}
  • id: 2359763
    {'lmfdb_iso': '47040.fx', 'p': 73, 'prec': 20, 'unit': 189930265465227350151804357731860365, 'val': 1}
  • id: 2359758
    {'lmfdb_iso': '47040.fx', 'p': 79, 'prec': 20, 'unit': 959088721191911720594411001003854476, 'val': 1}
  • id: 2359768
    {'lmfdb_iso': '47040.fx', 'p': 83, 'prec': 20, 'unit': 1592070858651503253044616654727563885, 'val': 1}
  • id: 2359765
    {'lmfdb_iso': '47040.fx', 'p': 89, 'prec': 20, 'unit': 746725703139778552689134742449067438, 'val': 1}
  • id: 2359750
    {'lmfdb_iso': '47040.fx', 'p': 97, 'prec': 20, 'unit': 31102059519993991249810598450076727494, 'val': 1}