Elliptic curve data - 7744.f1

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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': '7744l', 'Clabel': '7744l2', 'Cnumber': 2, 'abc_quality': 0.9461121308337243, 'absD': 6799340234604544, 'adelic_genus': 16, 'adelic_index': 480, 'adelic_level': 88, 'ainvs': [0, 1, 0, -19521, 4097311], 'analytic_rank': 0, 'bad_primes': [2, 11], 'class_deg': 11, 'class_size': 2, 'cm': 0, 'conductor': 7744, 'degree': 33792, 'elladic_images': ['4.2.0.1', '11.60.1.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7207075691234241467718805133', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 11, 'iso_nlabel': 5, 'isogeny_degrees': [1, 11], 'jinv': [-121, 1], 'lmfdb_iso': '7744.f', 'lmfdb_label': '7744.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -2, -7], 'min_quad_twist_disc': -88, 'modell_images': ['11B.10.4'], 'modm_images': ['4.2.0.a.1', '11.60.1.b.1', '44.240.6-44.b.1.1', '88.480.16.?'], 'nonmax_primes': [2, 11], 'nonmax_rad': 22, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 121], [11, 32, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3172592623818026040722539839', 'prec': 103}, 'szpiro_ratio': 4.911178679615941, '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, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 5, 0, 6, 0], 'aplist': [0, -2, -1, 2, 0, 1, 5, 6, 2, 9, -2, 3, 5, 0, 2, -9, -8, 6, -2, 12, 2, 10, 6, -9, -13], 'class_deg': 11, 'class_size': 2, 'conductor': 7744, 'isogeny_matrix': [[1, 11], [11, 1]], 'lmfdb_iso': '7744.f', 'trace_hash': 133404072526562710}
• 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': '0.032019341456770476212569502429', 'prec': 107}, 'conductor': 7744, 'gens': [], 'heights': [], 'lmfdb_label': '7744.f1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.36055193109294912707950093502', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4422077243717965083180037400900889632', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [0, 0], '7': [0, 0], '11': 'a', '13': [2, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '7744.f1'}
• ec_torsion_growth •

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

  
  
  • id: 405114
    {'degree': 3, 'field': [2, 4, -1, 1], 'lmfdb_label': '7744.f1', 'torsion': [2]}
  • id: 405115
    {'degree': 6, 'field': [4, 0, 20, 0, -7, 0, 1], 'lmfdb_label': '7744.f1', 'torsion': [2, 2]}
  • id: 405116
    {'degree': 8, 'field': [-5808, 0, -1672, 0, -264, 0, 0, 0, 1], 'lmfdb_label': '7744.f1', 'torsion': [3]}
  • id: 405117
    {'degree': 10, 'field': [-32, 0, 240, 0, -280, 0, 112, 0, -18, 0, 1], 'lmfdb_label': '7744.f1', 'torsion': [11]}
  • id: 405118
    {'degree': 12, 'field': [86, 424, 553, 262, -89, -72, 416, -344, 206, -80, 27, -6, 1], 'lmfdb_label': '7744.f1', 'torsion': [4]}
• 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: 159868
    {'conductor': 7744, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '7744.f1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 159869
    {'conductor': 7744, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '7744.f1', 'prime': 11, '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: 1715117
    {'adelic_gens': [[1, 84, 0, 1], [15, 0, 0, 39], [45, 44, 44, 45], [45, 33, 0, 67], [1, 0, 44, 1], [45, 22, 22, 1], [12, 55, 77, 23], [1, 44, 0, 1], [43, 44, 22, 87]], 'adelic_image': '88.480.16.?', 'conductor': 7744, 'lmfdb_label': '7744.f1', 'prime': 0}
  • id: 37954
    {'conductor': 7744, 'elladic_image': '4.2.0.1', 'lmfdb_label': '7744.f1', 'modell_image': '2G', 'prime': 2}
  • id: 37955
    {'conductor': 7744, 'elladic_image': '11.60.1.4', 'lmfdb_label': '7744.f1', 'modell_image': '11B.10.4', 'prime': 11}
• lmfdb_iso 7744.f does not appear in ec_padic