Elliptic curve data - 47040.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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '47040w', 'Clabel': '47040w1', 'Cnumber': 1, 'abc_quality': 1.0244474458248836, 'absD': 1624850834443468800000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 840, 'ainvs': [0, -1, 0, -3350881, 1347539425], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 47040, 'degree': 3010560, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7686902106412170047591430001', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [393349474783, 153600000], 'lmfdb_iso': '47040.a', 'lmfdb_label': '47040.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -1068, -8112], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '56.6.0.c.1', '120.6.0.?', '210.6.0.?', '840.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 105], [3, 4, 15680], [5, 6, 9408], [7, 20, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.26953682800981406180428026033', 'prec': 103}, 'szpiro_ratio': 5.26899370442707, '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, -6, 0, -6, 0, 1, 0, 0, 0, 4, 0], 'aplist': [0, -1, -1, 0, -6, -6, 0, 4, 0, 8, 2, -4, -10, 6, -2, -10, 4, -14, -14, 8, 6, -8, 8, -18, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 47040, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '47040.a', 'trace_hash': 988325597857453011}
• 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': '0.0039368261685086386797886187269', 'prec': 110}, 'conductor': 47040, 'gens': [], 'heights': [], 'lmfdb_label': '47040.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.13649917940819138612848470176', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.27299835881638277225696940351839031246', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[425, 0, 1]], 'xcoord_integral_points': [425]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '47040.a1'}
• ec_torsion_growth •

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

  
  
  • id: 2292316
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '47040.a1', 'torsion': [2, 2]}
  • id: 2292317
    {'degree': 4, 'field': [63, -28, 0, 0, 1], 'lmfdb_label': '47040.a1', 'torsion': [4]}
  • id: 2292320
    {'degree': 8, 'field': [-9408, 0, -1274, 0, 336, 0, 0, 0, 1], 'lmfdb_label': '47040.a1', 'torsion': [6]}
  • id: 2292319
    {'degree': 8, 'field': [36, 0, 186, 0, 97, 0, 4, 0, 1], 'lmfdb_label': '47040.a1', 'torsion': [2, 4]}
  • id: 2292318
    {'degree': 8, 'field': [676, 0, -10028, 0, 789, 0, -2, 0, 1], 'lmfdb_label': '47040.a1', 'torsion': [2, 4]}
  • id: 2292321
    {'degree': 16, 'field': [20779248, -18677568, 23690240, -10244416, 5675968, -681680, 256536, -27360, 11593, -6344, 4692, -2200, 670, -168, 44, -8, 1], 'lmfdb_label': '47040.a1', 'torsion': [8]}
  • id: 2292322
    {'degree': 16, 'field': [888890256, 348268464, -1236552156, 785967552, -260590496, 67879968, -39168108, 22303616, -5078532, 78756, 46322, 7248, 2454, -728, 9, -6, 1], 'lmfdb_label': '47040.a1', '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: 1121906
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 32, 'j_denominator_valuation': 14, 'kodaira_symbol': -26, 'lmfdb_label': '47040.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1121907
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '47040.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1121908
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '47040.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1121909
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '47040.a1', 'prime': 7, '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: 1977269
    {'adelic_gens': [[837, 4, 836, 5], [1, 2, 2, 5], [737, 106, 104, 735], [1, 4, 0, 1], [421, 4, 2, 9], [124, 1, 599, 0], [562, 1, 559, 0], [1, 0, 4, 1], [674, 1, 503, 0], [3, 4, 8, 11]], 'adelic_image': '840.12.0.?', 'conductor': 47040, 'lmfdb_label': '47040.a1', 'prime': 0}
  • id: 203210
    {'conductor': 47040, 'elladic_image': '2.3.0.1', 'lmfdb_label': '47040.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 47040.a does not appear in ec_padic