Elliptic curve data - 43681.a1

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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': '43681m', 'Clabel': '43681m3', 'Cnumber': 3, 'abc_quality': 1.0929566831983986, 'absD': 916791127892651, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 10450, 'ainvs': [0, 1, 1, -341599980, -2430217915988], 'analytic_rank': 1, 'bad_primes': [11, 19], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 43681, 'degree': 4320000, 'elladic_images': ['25.60.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1678762410810526246468509101', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 25, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5, 25], 'jinv': [-52893159101157376, 11], 'lmfdb_iso': '43681.a', 'lmfdb_label': '43681.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -7820, -263580], 'min_quad_twist_disc': 209, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '22.2.0.a.1', '25.60.0.a.2', '110.24.1.?', '190.24.0.?', '275.300.12.?', '550.600.37.?', '950.120.0.?', '1045.24.0.?', '2090.48.1.?', '5225.600.12.?', '10450.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '58.182560168273918498979522125', 'prec': 100}, 'semistable': False, 'serre_invariants': [[11, 72, 361], [19, 182, 121]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540517', 'prec': 103}, 'szpiro_ratio': 6.603953683138829, '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, -2, 1, 2, 1, -2, 2, 0, -2, -2, 0, 2, 4, -4, 1, -4, 2, 4, 0, 2], 'aplist': [-2, 1, 1, 2, 0, 4, 2, 0, -1, 0, -7, -3, -8, 6, 8, 6, -5, -12, 7, 3, -4, -10, 6, -15, 7], 'class_deg': 25, 'class_size': 3, 'conductor': 43681, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '43681.a', 'trace_hash': 899512665719563647}
• 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': '0.0017718120798621620265148389587', 'prec': 110}, 'conductor': 43681, 'gens': [[247885230620377230664447069, 2193566378819640710535957512322100964103, 98996992610]], 'heights': [{'__RealLiteral__': 0, 'data': '58.182560168273918498979522125', 'prec': 100}], 'lmfdb_label': '43681.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.017558608668871298162788971132', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0864192213911212869419328903439887364', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': [1, 0], '5': [3, 2], '7': [3, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': 'a', '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '43681.a1'}
• ec_torsion_growth •

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

  
  
  • id: 2141438
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '43681.a1', 'torsion': [2]}
  • id: 2141439
    {'degree': 4, 'field': [13781, -261, 261, -1, 1], 'lmfdb_label': '43681.a1', 'torsion': [5]}
  • id: 2141440
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '43681.a1', 'torsion': [2, 2]}
  • id: 2141441
    {'degree': 8, 'field': [-164007, -84303, 10257, 7125, -1017, -152, -3, 0, 1], 'lmfdb_label': '43681.a1', 'torsion': [3]}
  • id: 2141442
    {'degree': 10, 'field': [-352, 0, 0, 0, 0, -2761, 0, 0, 0, 0, 1], 'lmfdb_label': '43681.a1', 'torsion': [5]}
  • id: 2141443
    {'degree': 12, 'field': [-1761701, 1202504, 185926, -519210, 162055, 5524, 2944, 1192, -561, -80, 6, -2, 1], 'lmfdb_label': '43681.a1', 'torsion': [4]}
  • id: 2141444
    {'degree': 12, 'field': [223198061, -44161347, 14222220, -6044946, 552085, -155304, 58917, -668, 1109, -24, 28, -1, 1], 'lmfdb_label': '43681.a1', 'torsion': [10]}
  • id: 2141445
    {'degree': 20, 'field': [4455135690688736251, -1694989021681864370, 905914848586301400, -220944309087930285, 56908575686373400, -9730990140998676, 2660364152498965, -174171985954450, 78412866679895, -1498921479825, 1383873043696, -6218536060, 15043963275, -10541630, 102202650, -2706, 424380, 0, 990, 0, 1], 'lmfdb_label': '43681.a1', 'torsion': [25]}
• 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: 1039076
    {'conductor': 43681, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '43681.a1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1039077
    {'conductor': 43681, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '43681.a1', 'prime': 19, '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

  
  
  • id: 1955501
    {'adelic_gens': [[3514, 3705, 8835, 6934], [1, 0, 50, 1], [1540, 4959, 7277, 1863], [1, 50, 0, 1], [10401, 50, 10400, 51], [38, 41, 7891, 7689], [549, 0, 0, 10449]], 'adelic_image': '10450.1200.37.?', 'conductor': 43681, 'lmfdb_label': '43681.a1', 'prime': 0}
  • id: 190378
    {'conductor': 43681, 'elladic_image': '25.60.0.2', 'lmfdb_label': '43681.a1', 'modell_image': '5B.4.2', 'prime': 5}
• ec_padic •

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

  
  
  • id: 2178992
    {'lmfdb_iso': '43681.a', 'p': 5, 'prec': 20, 'unit': 94112259437821, 'val': 0}
  • id: 2178993
    {'lmfdb_iso': '43681.a', 'p': 7, 'prec': 20, 'unit': 531415845713131, 'val': 2}
  • id: 2178997
    {'lmfdb_iso': '43681.a', 'p': 13, 'prec': 20, 'unit': 1190229851053497827997, 'val': 1}
  • id: 2178999
    {'lmfdb_iso': '43681.a', 'p': 17, 'prec': 20, 'unit': 2309144658499618190740, 'val': 1}
  • id: 2179004
    {'lmfdb_iso': '43681.a', 'p': 23, 'prec': 20, 'unit': 73059331654352784196034138, 'val': 1}
  • id: 2178994
    {'lmfdb_iso': '43681.a', 'p': 31, 'prec': 20, 'unit': 17848615999436778680076347813, 'val': 1}
  • id: 2179009
    {'lmfdb_iso': '43681.a', 'p': 37, 'prec': 20, 'unit': 414990620739640698199473576900, 'val': 1}
  • id: 2178995
    {'lmfdb_iso': '43681.a', 'p': 41, 'prec': 20, 'unit': 3750670955109801609472019174213, 'val': 1}
  • id: 2178996
    {'lmfdb_iso': '43681.a', 'p': 43, 'prec': 20, 'unit': 1291803762353651086131233239809, 'val': 1}
  • id: 2179007
    {'lmfdb_iso': '43681.a', 'p': 47, 'prec': 20, 'unit': 47671437355675756947614062687454, 'val': 1}
  • id: 2179001
    {'lmfdb_iso': '43681.a', 'p': 53, 'prec': 20, 'unit': 559729939650754973716156529052623, 'val': 1}
  • id: 2179002
    {'lmfdb_iso': '43681.a', 'p': 59, 'prec': 20, 'unit': 3744079255598409376036630047671280, 'val': 1}
  • id: 2179008
    {'lmfdb_iso': '43681.a', 'p': 61, 'prec': 20, 'unit': 976647118599128747151984074744684, 'val': 1}
  • id: 2178991
    {'lmfdb_iso': '43681.a', 'p': 67, 'prec': 20, 'unit': 47380085619661065043980042796783113, 'val': 1}
  • id: 2179006
    {'lmfdb_iso': '43681.a', 'p': 71, 'prec': 20, 'unit': 105208310258882501176268676027544726, 'val': 1}
  • id: 2179003
    {'lmfdb_iso': '43681.a', 'p': 73, 'prec': 20, 'unit': 87831776426431741183225167000745745, 'val': 1}
  • id: 2178998
    {'lmfdb_iso': '43681.a', 'p': 79, 'prec': 20, 'unit': 103653630178005900934174253444242796, 'val': 1}
  • id: 2179000
    {'lmfdb_iso': '43681.a', 'p': 83, 'prec': 20, 'unit': 2298808787244995307500203877236344329, 'val': 1}
  • id: 2179005
    {'lmfdb_iso': '43681.a', 'p': 89, 'prec': 20, 'unit': 6004904872263945723700975320893527232, 'val': 1}
  • id: 2178990
    {'lmfdb_iso': '43681.a', 'p': 97, 'prec': 20, 'unit': 35580024204968723022469045219506014892, 'val': 1}