Elliptic curve data - 47040.r1

Formats: - HTML - YAML - JSON - 2025-09-21T05:33:42.365249

• 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': '47040e', 'Clabel': '47040e4', 'Cnumber': 4, 'abc_quality': 0.9761022274426737, 'absD': 109292720947200, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, -1, 0, -732321, 241456545], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 47040, 'degree': 393216, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9320022922544052388581819363', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [5633270409316, 14175], 'lmfdb_iso': '47040.r', 'lmfdb_label': '47040.r1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -3736, -86660], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.4', '24.24.0-24.z.1.3', '28.12.0.h.1', '56.24.0-28.h.1.1', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 23, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.94006300711258625968787285842', 'prec': 103}, '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': '0.034850976980154840415862735967', 'prec': 107}, 'szpiro_ratio': 4.844941067049751, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [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, 0, 0, -2, 0, 1, 0, -6, 0, -4, 0], 'aplist': [0, -1, -1, 0, 0, -2, -6, -4, 4, -6, 0, -6, -6, 4, -8, -14, -4, -2, -12, -12, -10, 8, -4, -6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 47040, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '47040.r', 'trace_hash': 2141028152274320075}
• 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': '0.020983799643809805594790248387', 'prec': 107}, 'conductor': 47040, 'gens': [[513, 720, 1], [488, 245, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.96855016564107874864347058652', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.97411399695039204263294583399', 'prec': 103}], 'lmfdb_label': '47040.r1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.51430402530692386937051872746', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.7356510176021522737959791570658775082', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[495, 0, 1]], 'xcoord_integral_points': [-639, 145, 243, 488, 495, 496, 513, 593, 639, 1553, 2259, 43713]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': 'a', '11': [2, 2, 0], '13': [2, 0], '17': [2, 0], '19': [2, 0], '23': [4, 0], '29': [2, 0], '31': [2, 2, 0], '37': [2, 0], '41': [2, 0], '43': [4, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '47040.r1'}
• ec_torsion_growth •

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

  
  
  • id: 2291910
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [4]}
  • id: 2291908
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [2, 2]}
  • id: 2291909
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [4]}
  • id: 2291911
    {'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [2, 4]}
  • id: 2291915
    {'degree': 8, 'field': [-91875, 0, 18550, 0, -1050, 0, 0, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [6]}
  • id: 2291913
    {'degree': 8, 'field': [1, 0, -18, 0, 62, 0, -18, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [8]}
  • id: 2291912
    {'degree': 8, 'field': [36, 0, 116, 0, -43, 0, 4, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [2, 4]}
  • id: 2291914
    {'degree': 8, 'field': [8281, 0, -1218, 0, -97, 0, 12, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [8]}
  • id: 2291917
    {'degree': 16, 'field': [1, 0, -28, 0, 242, 0, -840, 0, 1259, 0, -840, 0, 242, 0, -28, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [2, 8]}
  • id: 2291916
    {'degree': 16, 'field': [87616, 0, -63424, 0, 42772, 0, -11940, 0, 3561, 0, -360, 0, 22, 0, -4, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [4, 4]}
  • id: 2291918
    {'degree': 16, 'field': [167524, -373968, -355400, 743920, 560848, 428264, 566000, 173560, 67212, 35416, 3100, 2240, 508, -28, 48, -4, 1], 'lmfdb_label': '47040.r1', 'torsion': [2, 8]}
  • id: 2291921
    {'degree': 16, 'field': [1750329, 0, -35673372, 0, -4948020, 0, -560756, 0, 5390, 0, 1036, 0, 700, 0, -28, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [12]}
  • id: 2291920
    {'degree': 16, 'field': [5645376, 0, -5629824, 0, -858816, 0, 27328, 0, 31136, 0, 1288, 0, 364, 0, -4, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [12]}
  • id: 2291919
    {'degree': 16, 'field': [149744169, 0, -50577144, 0, -29670884, 0, -371568, 0, 409854, 0, -7576, 0, -804, 0, 0, 0, 1], 'lmfdb_label': '47040.r1', 'torsion': [2, 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: 1121742
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '47040.r1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1121743
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '47040.r1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1121744
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '47040.r1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1121745
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '47040.r1', '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: 1977766
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [88, 165, 139, 166], [7, 6, 162, 163], [161, 8, 160, 9], [113, 8, 116, 33], [24, 113, 49, 96], [101, 102, 134, 53], [1, 4, 4, 17]], 'adelic_image': '168.48.0.?', 'conductor': 47040, 'lmfdb_label': '47040.r1', 'prime': 0}
  • id: 203692
    {'conductor': 47040, 'elladic_image': '8.12.0.8', 'lmfdb_label': '47040.r1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2357975
    {'lmfdb_iso': '47040.r', 'p': 13, 'prec': 20, 'unit': 472167659229433512744, 'val': 2}
  • id: 2357977
    {'lmfdb_iso': '47040.r', 'p': 17, 'prec': 20, 'unit': 238558720459304028060144, 'val': 2}
  • id: 2357978
    {'lmfdb_iso': '47040.r', 'p': 19, 'prec': 20, 'unit': 1866069924075969019372093, 'val': 2}
  • id: 2357982
    {'lmfdb_iso': '47040.r', 'p': 23, 'prec': 20, 'unit': 1998858774450609545076917, 'val': 3}
  • id: 2357974
    {'lmfdb_iso': '47040.r', 'p': 29, 'prec': 20, 'unit': 3663631900892423971565666648, 'val': 2}
  • id: 2357970
    {'lmfdb_iso': '47040.r', 'p': 37, 'prec': 20, 'unit': 373708731044610344466811860912, 'val': 2}
  • id: 2357972
    {'lmfdb_iso': '47040.r', 'p': 41, 'prec': 20, 'unit': 553098104803526673248554732695, 'val': 2}
  • id: 2357973
    {'lmfdb_iso': '47040.r', 'p': 43, 'prec': 20, 'unit': 41817517548380364101155255981, 'val': 3}
  • id: 2357984
    {'lmfdb_iso': '47040.r', 'p': 47, 'prec': 20, 'unit': 42999841346295608855290488524864, 'val': 2}
  • id: 2357979
    {'lmfdb_iso': '47040.r', 'p': 53, 'prec': 20, 'unit': 387899164089864778452148387751734, 'val': 2}
  • id: 2357980
    {'lmfdb_iso': '47040.r', 'p': 59, 'prec': 20, 'unit': 1817583336554514143457563015282464, 'val': 2}
  • id: 2357985
    {'lmfdb_iso': '47040.r', 'p': 61, 'prec': 20, 'unit': 4762546480887794430162610265858428, 'val': 2}
  • id: 2357969
    {'lmfdb_iso': '47040.r', 'p': 67, 'prec': 20, 'unit': 14363027839209058803069456898726886, 'val': 2}
  • id: 2357971
    {'lmfdb_iso': '47040.r', 'p': 71, 'prec': 20, 'unit': 4265317244494563198188751631332463, 'val': 2}
  • id: 2357981
    {'lmfdb_iso': '47040.r', 'p': 73, 'prec': 20, 'unit': 155773951771106294575361329537144144, 'val': 2}
  • id: 2357976
    {'lmfdb_iso': '47040.r', 'p': 79, 'prec': 20, 'unit': 205987689389177766093630230219790778, 'val': 2}
  • id: 2357968
    {'lmfdb_iso': '47040.r', 'p': 83, 'prec': 20, 'unit': 899851404953901608602834075826758328, 'val': 2}
  • id: 2357983
    {'lmfdb_iso': '47040.r', 'p': 89, 'prec': 20, 'unit': 3864699288210619814428477875245074923, 'val': 2}
  • id: 2357967
    {'lmfdb_iso': '47040.r', 'p': 97, 'prec': 20, 'unit': 32409219549632744641682160657724405503, 'val': 2}