Elliptic curve data - 32144.b1

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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': '32144bf', 'Clabel': '32144bf2', 'Cnumber': 2, 'abc_quality': 1.0684325259249097, 'absD': 5255610989765603590144, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 2296, 'ainvs': [0, 0, 0, -7535269147, -251765528891702], 'analytic_rank': 0, 'bad_primes': [2, 7, 41], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 32144, 'degree': 28449792, 'elladic_images': ['7.24.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.0368429677121421652939382805', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 7, 'iso_nlabel': 1, 'isogeny_degrees': [1, 7], 'jinv': [98191033604529537629349729, 10906239337336], 'lmfdb_iso': '32144.b', 'lmfdb_label': '32144.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -9611313, -11466507927], 'min_quad_twist_disc': 28, 'modell_images': ['7B.6.3'], 'modm_images': ['7.24.0.a.2', '28.48.0-7.a.2.2', '2296.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2009], [7, 32, 16], [41, 42, 784]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.3707407126245402033240297873', 'prec': 100}, 'szpiro_ratio': 7.693421632479556, '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, -3, 0, 1, 0, 0, 0, 6, 0, 2, 0, 0, 0, -3, 0, 3, 0, -8, 0], 'aplist': [0, -3, 1, 0, 2, 0, 3, -8, 4, -5, -3, 10, 1, 5, 6, -9, -10, -13, 2, -9, -4, 11, -14, 1, -7], 'class_deg': 7, 'class_size': 2, 'conductor': 32144, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '32144.b', 'trace_hash': 1622168294866006010}
• 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': '0.00031163250423732772640632509522', 'prec': 113}, 'conductor': 32144, 'gens': [], 'heights': [], 'lmfdb_label': '32144.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.016204098049082044405584480349', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.90742949074859448671273089952793682024', 'prec': 133}, 'tamagawa_product': 56, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0, 0], '5': [2, 0], '7': 'a', '11': [0, 0], '13': [0, 0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [1, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '32144.b1'}
• ec_torsion_growth •

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

  
  
  • id: 1600597
    {'degree': 3, 'field': [-14, -14, -1, 1], 'lmfdb_label': '32144.b1', 'torsion': [2]}
  • id: 1600599
    {'degree': 6, 'field': [1, 0, 6, 0, 5, 0, 1], 'lmfdb_label': '32144.b1', 'torsion': [7]}
  • id: 1600598
    {'degree': 6, 'field': [8, -8, -94, 144, -47, -2, 1], 'lmfdb_label': '32144.b1', 'torsion': [2, 2]}
  • id: 1600600
    {'degree': 8, 'field': [-28812, 0, 5145, 0, -588, 0, 0, 0, 1], 'lmfdb_label': '32144.b1', 'torsion': [3]}
  • id: 1600601
    {'degree': 12, 'field': [9184, 0, -80028, 0, -48735, 0, -7020, 0, -570, 0, 0, 0, 1], 'lmfdb_label': '32144.b1', 'torsion': [4]}
  • id: 1600602
    {'degree': 14, 'field': [-28672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '32144.b1', 'torsion': [7]}
  • id: 1600603
    {'degree': 18, 'field': [5832, -33048, 93636, -118476, 78912, -54600, 245833, -240860, 123680, -32972, 23370, -19128, 9632, -2408, 365, -64, 32, -8, 1], 'lmfdb_label': '32144.b1', 'torsion': [14]}
• 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: 751280
    {'conductor': 32144, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '32144.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 751281
    {'conductor': 32144, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '32144.b1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 751282
    {'conductor': 32144, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '32144.b1', 'prime': 41, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
• ec_galrep •

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

  
  
  • id: 1878726
    {'adelic_gens': [[1721, 2282, 567, 2197], [2283, 14, 2282, 15], [1, 14, 0, 1], [785, 14, 903, 99], [1149, 14, 1155, 99], [1, 0, 14, 1], [8, 5, 91, 57], [1719, 648, 525, 279]], 'adelic_image': '2296.96.2.?', 'conductor': 32144, 'lmfdb_label': '32144.b1', 'prime': 0}
  • id: 143548
    {'conductor': 32144, 'elladic_image': '7.24.0.2', 'lmfdb_label': '32144.b1', 'modell_image': '7B.6.3', 'prime': 7}
• lmfdb_iso 32144.b does not appear in ec_padic