Elliptic curve data - 299538.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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '299538a', 'Clabel': '299538a1', 'Cnumber': 1, 'abc_quality': 1.2854862760382055, 'absD': 32769946046016, 'adelic_genus': 1, 'adelic_index': 128, 'adelic_level': 516, 'ainvs': [1, -1, 0, 7974, -29324], 'analytic_rank': 0, 'bad_primes': [2, 3, 43], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 299538, 'degree': 943488, 'elladic_images': ['4.8.0.2', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2827935719041918690426305245', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [109503, 64], 'lmfdb_iso': '299538.a', 'lmfdb_label': '299538.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 39, -19], 'min_quad_twist_disc': 129, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '4.8.0.b.1', '12.64.1.b.1', '129.8.0.?', '172.16.0.?', '516.128.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.96401058216529257315887247782', 'prec': 107}, 'szpiro_ratio': 3.0583162231816603, '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, 0, 1, -3, 0, 4, -1, 0, 3, 0, 0, -1, -4, 0, 1, 3, 0, 4, -3], 'aplist': [-1, 0, -3, 4, 0, -1, 3, 4, 0, 9, -4, 1, -6, 0, 12, 6, 0, 1, -4, -12, -11, -16, 12, -3, 2], 'class_deg': 3, 'class_size': 2, 'conductor': 299538, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '299538.a', 'trace_hash': 2272975487905088108}
• 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': '0.076874032076587163602007484561', 'prec': 107}, 'conductor': 299538, 'gens': [], 'heights': [], 'lmfdb_label': '299538.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.38699715642544514921865416428', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5479886257017805968746166571330281971', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 299538.a2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12679935
    {'degree': 2, 'field': [11, -1, 1], 'lmfdb_label': '299538.a2', 'torsion': [3]}
  • id: 12679936
    {'degree': 3, 'field': [-4, -3, 0, 1], 'lmfdb_label': '299538.a2', 'torsion': [2]}
  • id: 12679938
    {'degree': 6, 'field': [-21591, -3690, 702, -68, -66, 0, 1], 'lmfdb_label': '299538.a2', 'torsion': [4]}
  • id: 12679940
    {'degree': 6, 'field': [-3000, 0, 0, -99, 0, 0, 1], 'lmfdb_label': '299538.a2', 'torsion': [3]}
  • id: 12679937
    {'degree': 6, 'field': [2, 6, 9, -2, 0, 0, 1], 'lmfdb_label': '299538.a2', 'torsion': [2, 2]}
  • id: 12679939
    {'degree': 6, 'field': [2279, -645, 384, -47, 30, -3, 1], 'lmfdb_label': '299538.a2', 'torsion': [12]}
  • id: 12679942
    {'degree': 12, 'field': [1766656, -976224, 1194876, -463930, 300345, -87204, 37847, -7926, 2490, -350, 81, -6, 1], 'lmfdb_label': '299538.a2', 'torsion': [3, 3]}
  • id: 12679941
    {'degree': 12, 'field': [2123021, -1132902, 1124205, -457554, 281214, -86622, 37201, -7974, 2490, -346, 81, -6, 1], 'lmfdb_label': '299538.a2', 'torsion': [4, 12]}
  • id: 12679944
    {'degree': 18, 'field': [-25308601856, 0, 0, -2288206776, 0, 0, 68590428, 0, 0, 283241, 0, 0, -19515, 0, 0, -111, 0, 0, 1], 'lmfdb_label': '299538.a2', 'torsion': [6]}
  • id: 12679943
    {'degree': 18, 'field': [9567914723, -4988493279, 6223238757, -2656071210, 1824361128, -654952950, 320801568, -97604946, 37277037, -9583475, 2964429, -634842, 160758, -27720, 5688, -732, 117, -9, 1], 'lmfdb_label': '299538.a2', '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: 7420109
    {'conductor': 299538, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '299538.a2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7420110
    {'conductor': 299538, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '299538.a2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7420111
    {'conductor': 299538, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '299538.a2', 'prime': 43, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 3548355
    {'adelic_gens': [[259, 387, 0, 1], [345, 172, 344, 173], [1, 129, 129, 130], [345, 172, 172, 345], [1, 0, 216, 1], [83, 0, 0, 515], [301, 216, 300, 301]], 'adelic_image': '516.128.1.?', 'conductor': 299538, 'lmfdb_label': '299538.a2', 'prime': 0}
  • id: 1056673
    {'conductor': 299538, 'elladic_image': '4.8.0.2', 'lmfdb_label': '299538.a2', 'modell_image': '2G', 'prime': 2}
  • id: 1056674
    {'conductor': 299538, 'elladic_image': '3.4.0.1', 'lmfdb_label': '299538.a2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 299538.a does not appear in ec_padic