Elliptic curve data - 309738.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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '309738b', 'Clabel': '309738b2', 'Cnumber': 2, 'abc_quality': 1.0613853630417616, 'absD': 412674793337954973855744, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 2508, 'ainvs': [1, 1, 0, -150478829, 709760046621], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 13, 19], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 309738, 'degree': 67184640, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4465619830038454448364596852', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [1043861123787821767587211633, 1143143471850290786304], 'lmfdb_iso': '309738.b', 'lmfdb_label': '309738.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -150478829, 709760046621], 'min_quad_twist_disc': 1, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '44.2.0.a.1', '57.8.0-3.a.1.2', '132.8.0.?', '2508.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.9558221531427720348349551132', 'prec': 100}, 'szpiro_ratio': 5.38630114830329, '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, -1, -1, 1, -3, 1, -1, -1, 1, 3, -1, -1, -1, 1, 3, 1, 0, -1, 0, -3], 'aplist': [-1, -1, -3, -1, -1, -1, 0, 0, -6, 0, 4, 7, 0, -4, -6, 9, 0, 2, -2, 12, -10, 1, -3, 6, 19], 'class_deg': 3, 'class_size': 2, 'conductor': 309738, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '309738.b', 'trace_hash': 1787146366919903458}
• 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': '0.0010147388745830686755572183292', 'prec': 110}, 'conductor': 309738, 'gens': [], 'heights': [], 'lmfdb_label': '309738.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.094157524172452310705309824959', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.75326019337961848564247859967224477299', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 309738.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13067386
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '309738.b1', 'torsion': [3]}
  • id: 13067387
    {'degree': 3, 'field': [-76, -38, 0, 1], 'lmfdb_label': '309738.b1', 'torsion': [2]}
  • id: 13067390
    {'degree': 6, 'field': [-12, 33, 151, 8, -36, -1, 1], 'lmfdb_label': '309738.b1', 'torsion': [6]}
  • id: 13067388
    {'degree': 6, 'field': [-11, 0, 103, 0, -29, 0, 1], 'lmfdb_label': '309738.b1', 'torsion': [2, 2]}
  • id: 13067389
    {'degree': 6, 'field': [1539, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '309738.b1', 'torsion': [3]}
  • id: 13067393
    {'degree': 12, 'field': [-512, -6400, -5824, 72256, 39360, -34976, -21164, 2912, 2604, 20, -91, -2, 1], 'lmfdb_label': '309738.b1', 'torsion': [2, 6]}
  • id: 13067392
    {'degree': 12, 'field': [3136, 336, 876, -2330, 945, 216, 27, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '309738.b1', 'torsion': [3, 3]}
  • id: 13067391
    {'degree': 12, 'field': [63536, -518396, -71478, 197828, -40071, -53428, 6916, 6308, 266, -152, -38, 0, 1], 'lmfdb_label': '309738.b1', 'torsion': [4]}
  • id: 13067395
    {'degree': 18, 'field': [53706332, -17606640, -21137193, 30167315, -6465975, -5669172, 7699585, -4192155, 1660194, -381781, 63090, -7251, 7662, -3621, 1587, -366, 81, -9, 1], 'lmfdb_label': '309738.b1', 'torsion': [6]}
  • id: 13067394
    {'degree': 18, 'field': [63264711984203413, -25347279149469681, -15798576876499830, 126762848425082, 2043957260549217, 518814749578557, 6950570210162, -13129499282055, -1319411347578, 98672653157, 19021098954, -131233359, -122197114, -1095927, 473565, 6518, -996, -9, 1], 'lmfdb_label': '309738.b1', 'torsion': [9]}
• 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: 7669396
    {'conductor': 309738, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '309738.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7669397
    {'conductor': 309738, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '309738.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7669398
    {'conductor': 309738, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '309738.b1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7669399
    {'conductor': 309738, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '309738.b1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7669400
    {'conductor': 309738, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '309738.b1', 'prime': 19, '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: 3608788
    {'adelic_gens': [[2115, 2, 1198, 7], [1, 6, 0, 1], [4, 3, 9, 7], [3, 4, 8, 11], [1, 0, 6, 1], [1466, 1047, 1891, 7], [1255, 6, 1257, 19], [1597, 6, 2283, 19], [2503, 6, 2502, 7]], 'adelic_image': '2508.16.0.?', 'conductor': 309738, 'lmfdb_label': '309738.b1', 'prime': 0}
  • id: 1087589
    {'conductor': 309738, 'elladic_image': '3.4.0.1', 'lmfdb_label': '309738.b1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 309738.b does not appear in ec_padic