Elliptic curve data - 206310.ba3

Formats: - HTML - YAML - JSON - 2025-10-27T17:52:15.544324

• 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': '206310bo', 'Clabel': '206310bo2', 'Cnumber': 2, 'abc_quality': 1.0072076908890615, 'absD': 974143417127961600, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2760, 'ainvs': [1, 0, 1, -2861108, -1862360782], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 206310, 'degree': 7208960, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4184369946554492972874592748', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2], 'jinv': [17496824387403529, 6580454400], 'lmfdb_iso': '206310.ba', 'lmfdb_label': '206310.ba3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5409, 152596], 'min_quad_twist_disc': -23, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '24.12.0.b.1', '40.12.0.a.1', '60.12.0.b.1', '120.24.0.?', '184.12.0.?', '276.12.0.?', '460.12.0.?', '552.24.0.?', '920.24.0.?', '1380.24.0.?', '2760.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 529], [3, 4, 68770], [5, 6, 20631], [13, 14, 15870], [23, 266, 390]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.85068988669087445188408285890', 'prec': 103}, 'szpiro_ratio': 4.59370271766481, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
• 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, 1, -1, -4, -1, 1, -1, 0, 1, -1, 4, 1, 1, 2, -1, -4, 1], 'aplist': [-1, 1, 1, -4, 0, -1, 2, -4, 0, 2, -8, -2, -6, -12, 0, -10, 0, 10, 4, -16, -6, 8, 4, 14, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 206310, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '206310.ba', 'trace_hash': 1380437010539500120}
• 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': '0.0079318102610059614487258641949', 'prec': 110}, 'conductor': 206310, 'gens': [], 'heights': [], 'lmfdb_label': '206310.ba3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.11608492160087526399201114480', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.46433968640350105596804457921883598599', 'prec': 133}, 'tamagawa_product': 64, 'torsion_generators': [[-991, 495, 1], [1953, -977, 1]], 'xcoord_integral_points': [-991, 1953]}
• lmfdb_label 206310.ba3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9023640
    {'degree': 4, 'field': [100, 0, -26, 0, 1], 'lmfdb_label': '206310.ba3', 'torsion': [2, 4]}
  • id: 9023638
    {'degree': 4, 'field': [196, 0, 18, 0, 1], 'lmfdb_label': '206310.ba3', 'torsion': [2, 4]}
  • id: 9023639
    {'degree': 4, 'field': [2116, 0, -23, 0, 1], 'lmfdb_label': '206310.ba3', 'torsion': [2, 4]}
  • id: 9023641
    {'degree': 8, 'field': [-7021296, 2925504, -1142172, 87692, -16364, 116, 34, -4, 1], 'lmfdb_label': '206310.ba3', 'torsion': [2, 6]}
  • id: 9023642
    {'degree': 16, 'field': [585225, 0, 903420, 0, 556686, 0, -81672, 0, 13459, 0, 744, 0, 374, 0, -12, 0, 1], 'lmfdb_label': '206310.ba3', 'torsion': [4, 4]}
  • id: 9023643
    {'degree': 16, 'field': [2952586460, -644926800, 717968680, -154018240, 97675936, -27188872, 13235940, -3969760, 1504661, -374840, 109376, -20120, 4506, -560, 100, -8, 1], 'lmfdb_label': '206310.ba3', 'torsion': [2, 8]}
  • id: 9023645
    {'degree': 16, 'field': [3236983500, 6851984400, -6143276760, -1336742400, 474351592, 211764568, -36666436, -26761440, 3883813, 1738232, -217688, -67288, 8242, 1344, -172, -8, 1], 'lmfdb_label': '206310.ba3', 'torsion': [2, 8]}
  • id: 9023644
    {'degree': 16, 'field': [129322621221, -37261974678, -8117526552, -4126177338, 1934347999, -68543218, 94687652, -17971632, 2454268, -815522, 107332, -16994, 3895, -294, 104, -4, 1], 'lmfdb_label': '206310.ba3', 'torsion': [2, 8]}
• 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: 5108772
    {'conductor': 206310, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '206310.ba3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5108773
    {'conductor': 206310, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '206310.ba3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5108774
    {'conductor': 206310, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '206310.ba3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5108775
    {'conductor': 206310, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '206310.ba3', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5108776
    {'conductor': 206310, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '206310.ba3', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2984157
    {'adelic_gens': [[1, 0, 4, 1], [2757, 4, 2756, 5], [1, 4, 0, 1], [1657, 2162, 0, 1], [2163, 2162, 2438, 599], [1559, 0, 0, 2759], [1381, 1564, 2162, 369], [93, 1564, 782, 2163]], 'adelic_image': '2760.48.0.?', 'conductor': 206310, 'lmfdb_label': '206310.ba3', 'prime': 0}
  • id: 762081
    {'conductor': 206310, 'elladic_image': '2.6.0.1', 'lmfdb_label': '206310.ba3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 206310.ba does not appear in ec_padic