Elliptic curve data - 45504.bl1

Formats: - HTML - YAML - JSON - 2025-10-26T09:08:16.723359

• 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': '45504br', 'Clabel': '45504br2', 'Cnumber': 2, 'abc_quality': 1.0196212670962481, 'absD': 9408554162699894784, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 9480, 'ainvs': [0, 0, 0, -13466892, -19021121008], 'analytic_rank': 0, 'bad_primes': [2, 3, 79], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 45504, 'degree': 1382400, 'elladic_images': ['5.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7311365191811978093983030437', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 5, 'iso_nlabel': 37, 'isogeny_degrees': [1, 5], 'jinv': [1413378216646643521, 49232902384], 'lmfdb_iso': '45504.bl', 'lmfdb_label': '45504.bl1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -23380, -1385691], 'min_quad_twist_disc': 24, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '120.24.0.?', '316.2.0.?', '1580.24.1.?', '9480.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 711], [3, 2, 5056], [5, 2, 576], [79, 80, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1421096040072249995748322431', 'prec': 100}, 'szpiro_ratio': 5.674376242649809, '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, 1, 0, -3, 0, 0, 0, -2, 0, 1, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, 1, -3, -2, 1, 2, 0, -6, -10, -2, 2, -2, 4, 3, 4, -5, -12, 8, -13, -6, 1, 6, 15, 13], 'class_deg': 5, 'class_size': 2, 'conductor': 45504, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '45504.bl', 'trace_hash': 11853202800262731}
• 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': '0.0042438982295400514884150639492', 'prec': 110}, 'conductor': 45504, 'gens': [], 'heights': [], 'lmfdb_label': '45504.bl1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.078810415662021097973831464233', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.78810415662021097973831464232684906149', 'prec': 133}, 'tamagawa_product': 10, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 1], '7': [0, 0], '11': [0, 0], '13': [2, 0], '17': [0, 0], '19': [0, 0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0], '79': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '45504.bl1'}
• ec_torsion_growth •

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

  
  
  • id: 2222335
    {'degree': 3, 'field': [2, -4, -1, 1], 'lmfdb_label': '45504.bl1', 'torsion': [2]}
  • id: 2222336
    {'degree': 4, 'field': [180, 0, 30, 0, 1], 'lmfdb_label': '45504.bl1', 'torsion': [5]}
  • id: 2222337
    {'degree': 6, 'field': [8, -8, -34, 54, -17, -2, 1], 'lmfdb_label': '45504.bl1', 'torsion': [2, 2]}
  • id: 2222338
    {'degree': 8, 'field': [-972, 0, 378, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '45504.bl1', 'torsion': [3]}
  • id: 2222339
    {'degree': 10, 'field': [-486, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '45504.bl1', 'torsion': [5]}
  • id: 2222340
    {'degree': 12, 'field': [551338, -299728, -158549, 78286, -12327, 9576, -3746, 900, -516, 152, -9, -2, 1], 'lmfdb_label': '45504.bl1', 'torsion': [4]}
  • id: 2222341
    {'degree': 12, 'field': [20257456, -4203488, 5692672, -937008, 726604, -110744, 60228, -7208, 2935, -248, 80, -4, 1], 'lmfdb_label': '45504.bl1', 'torsion': [10]}
• 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: 1083749
    {'conductor': 45504, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '45504.bl1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1083750
    {'conductor': 45504, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '45504.bl1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1083751
    {'conductor': 45504, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '45504.bl1', 'prime': 79, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
• ec_galrep •

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

  
  
  • id: 1967234
    {'adelic_gens': [[6, 13, 9425, 9361], [6319, 0, 0, 9479], [1589, 3150, 1590, 3149], [1, 0, 10, 1], [6481, 6330, 7125, 3211], [4739, 0, 0, 9479], [7117, 6330, 7860, 6421], [2369, 3150, 8685, 6269], [6314, 3147, 1635, 4859], [9471, 10, 9470, 11], [1, 10, 0, 1]], 'adelic_image': '9480.48.1.?', 'conductor': 45504, 'lmfdb_label': '45504.bl1', 'prime': 0}
  • id: 197200
    {'conductor': 45504, 'elladic_image': '5.12.0.2', 'lmfdb_label': '45504.bl1', 'modell_image': '5B.4.2', 'prime': 5}
• lmfdb_iso 45504.bl does not appear in ec_padic