Elliptic curve data - 88752.a2

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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': '88752n', 'Clabel': '88752n1', 'Cnumber': 1, 'abc_quality': 0.9991827355469977, 'absD': 3529718292754294898688, 'adelic_genus': 9, 'adelic_index': 336, 'adelic_level': 4472, 'ainvs': [0, -1, 0, -39302960, -94868756544], 'analytic_rank': 0, 'bad_primes': [2, 3, 43], 'class_deg': 13, 'class_size': 2, 'cm': 0, 'conductor': 88752, 'degree': 13523328, 'elladic_images': ['8.2.0.1', '13.28.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0849400815290713730770673260', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 13], 'jinv': [-140246460241, 73728], 'lmfdb_iso': '88752.a', 'lmfdb_label': '88752.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -1328, -19200], 'min_quad_twist_disc': 172, 'modell_images': ['13B.4.1'], 'modm_images': ['8.2.0.a.1', '13.28.0.a.1', '52.56.0-13.a.1.1', '104.112.1.?', '559.84.2.?', '2236.168.2.?', '4472.336.9.?'], 'nonmax_primes': [2, 13], 'nonmax_rad': 26, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1849], [3, 4, 29584], [43, 674, 48]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.11567384282658221865539313769', 'prec': 107}, 'szpiro_ratio': 5.623765557032923, '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, -1, 0, -4, 0, -4, 0, 1, 0, 1, 0, -4, 0, 4, 0, -5, 0, -5, 0], 'aplist': [0, -1, -4, -4, 1, -4, -5, -5, -2, -8, 4, -2, 3, 0, 4, 12, 5, 10, 5, 12, 7, 14, 4, -15, -19], 'class_deg': 13, 'class_size': 2, 'conductor': 88752, 'isogeny_matrix': [[1, 13], [13, 1]], 'lmfdb_iso': '88752.a', 'trace_hash': 908075288964093746}
• 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': '0.0020914866228587213273299426389', 'prec': 110}, 'conductor': 88752, 'gens': [], 'heights': [], 'lmfdb_label': '88752.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.030147378199397480090163673389', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999999', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '0.12058951279758992036065469355444458447', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [2, 0], '7': [0, 0], '11': [4, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': 'a', '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '88752.a2'}
• ec_torsion_growth •

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

  
  
  • id: 4155175
    {'degree': 3, 'field': [78, -14, -1, 1], 'lmfdb_label': '88752.a2', 'torsion': [2]}
  • id: 4155177
    {'degree': 6, 'field': [64, 0, 180, 0, 29, 0, 1], 'lmfdb_label': '88752.a2', 'torsion': [13]}
  • id: 4155176
    {'degree': 6, 'field': [1458, 0, 333, 0, -28, 0, 1], 'lmfdb_label': '88752.a2', 'torsion': [2, 2]}
  • id: 4155178
    {'degree': 8, 'field': [-192, 0, 16, 0, 48, 0, 0, 0, 1], 'lmfdb_label': '88752.a2', 'torsion': [3]}
  • id: 4155179
    {'degree': 12, 'field': [-128, 0, -4897, 0, -1747, 0, -274, 0, 146, 0, -13, 0, 1], 'lmfdb_label': '88752.a2', 'torsion': [4]}
  • id: 4155180
    {'degree': 18, 'field': [1024, 0, 10304, 0, -3808, 0, -3404, 0, 2684, 0, -495, 0, -248, 0, 138, 0, -20, 0, 1], 'lmfdb_label': '88752.a2', 'torsion': [26]}
• 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: 2169856
    {'conductor': 88752, 'conductor_valuation': 4, 'discriminant_valuation': 25, 'j_denominator_valuation': 13, 'kodaira_symbol': -21, 'lmfdb_label': '88752.a2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2169857
    {'conductor': 88752, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '88752.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2169858
    {'conductor': 88752, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '88752.a2', 'prime': 43, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 2248740
    {'adelic_gens': [[705, 4446, 4056, 945], [4447, 26, 4446, 27], [1, 26, 0, 1], [14, 23, 871, 1431], [2222, 4459, 1131, 12], [14, 13, 2223, 4460], [1119, 2262, 0, 431], [1, 0, 26, 1]], 'adelic_image': '4472.336.9.?', 'conductor': 88752, 'lmfdb_label': '88752.a2', 'prime': 0}
  • id: 361293
    {'conductor': 88752, 'elladic_image': '8.2.0.1', 'lmfdb_label': '88752.a2', 'modell_image': '2G', 'prime': 2}
  • id: 361294
    {'conductor': 88752, 'elladic_image': '13.28.0.1', 'lmfdb_label': '88752.a2', 'modell_image': '13B.4.1', 'prime': 13}
• lmfdb_iso 88752.a does not appear in ec_padic