Elliptic curve data - 286650.ba1

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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': '286650ba', 'Clabel': '286650ba4', 'Cnumber': 4, 'abc_quality': 1.0218494599601673, 'absD': 6669069711547851562500000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 10920, 'ainvs': [1, -1, 0, -1202168067, -16042599251659], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 286650, 'degree': 141557760, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8539444729186097414629755385', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2, 4], 'jinv': [143378317900125424089, 4976562500000], 'lmfdb_iso': '286650.ba', 'lmfdb_label': '286650.ba1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -109040, -13831200], 'min_quad_twist_disc': 105, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '40.12.0.y.1', '104.12.0.?', '168.12.0.?', '520.24.0.?', '840.24.0.?', '2184.24.0.?', '5460.12.0.?', '10920.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.375740554408373352504647268', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 143325], [3, 6, 31850], [5, 18, 5733], [7, 32, 5850], [13, 14, 22050]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5269642978398480559122968817', 'prec': 100}, 'szpiro_ratio': 5.915619808689158, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [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, 0, 1, 0, 0, 0, -1, 0, 0, -4, 0, -1, 0, 0, 1, -2, 0, 4, 0], 'aplist': [-1, 0, 0, 0, -4, -1, -2, 4, 8, 2, -4, -10, -6, 0, -8, 2, 12, 2, 4, -12, -2, -8, -4, 2, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 286650, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '286650.ba', 'trace_hash': 907165286972329072}
• 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': '0.00044926890774155344567393046404', 'prec': 113}, 'conductor': 286650, 'gens': [[241525, 117279229, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '11.375740554408373352504647268', 'prec': 100}], 'lmfdb_label': '286650.ba1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.025639477006184012075365371067', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6666886139690952661382518047180020164', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-80429, 80429, 2]], 'xcoord_integral_points': [241525]}
• lmfdb_label 286650.ba1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12179270
    {'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '286650.ba1', 'torsion': [2, 2]}
  • id: 12179271
    {'degree': 2, 'field': [210, 0, 1], 'lmfdb_label': '286650.ba1', 'torsion': [4]}
  • id: 12179272
    {'degree': 2, 'field': [1365, 0, 1], 'lmfdb_label': '286650.ba1', 'torsion': [4]}
  • id: 12179273
    {'degree': 4, 'field': [3481, 0, 92, 0, 1], 'lmfdb_label': '286650.ba1', 'torsion': [2, 4]}
  • id: 12179274
    {'degree': 8, 'field': [-18943760, 18403840, -3047376, -133952, 7964, -1456, -236, 0, 1], 'lmfdb_label': '286650.ba1', 'torsion': [2, 4]}
  • id: 12179277
    {'degree': 8, 'field': [-75369, 77595, -29007, 10362, -612, 288, 9, -3, 1], 'lmfdb_label': '286650.ba1', 'torsion': [6]}
  • id: 12179275
    {'degree': 8, 'field': [9235, -460, 654, -384, 183, 8, 2, -4, 1], 'lmfdb_label': '286650.ba1', 'torsion': [8]}
  • id: 12179276
    {'degree': 8, 'field': [422500, 0, -33800, 0, 3341, 0, -52, 0, 1], 'lmfdb_label': '286650.ba1', 'torsion': [8]}
  • id: 12179281
    {'degree': 16, 'field': [-5821793525705, -3281854223850, -47272000981, 147760429986, 2793193249, -2337345852, -6734494, -36545892, 4739950, 4362132, -691810, -77124, 12079, 1614, -181, -6, 1], 'lmfdb_label': '286650.ba1', 'torsion': [2, 6]}
  • id: 12179282
    {'degree': 16, 'field': [350464, 0, 832393160, 0, 481175044, 0, 199327184, 0, -3343760, 0, -22708, 0, 8428, 0, -178, 0, 1], 'lmfdb_label': '286650.ba1', 'torsion': [12]}
  • id: 12179280
    {'degree': 16, 'field': [430536625, -1051788800, 992455536, -371614968, 15148558, 18195104, -6181764, 3901008, -104625, -95808, 22980, -8992, 1006, 144, -12, -8, 1], 'lmfdb_label': '286650.ba1', 'torsion': [2, 8]}
  • id: 12179279
    {'degree': 16, 'field': [12463489600, 0, -459204480, 0, -414465824, 0, 37858368, 0, 14679444, 0, 862584, 0, 20704, 0, 228, 0, 1], 'lmfdb_label': '286650.ba1', 'torsion': [2, 8]}
  • id: 12179283
    {'degree': 16, 'field': [961041285684, -601113869064, 244496456532, -81612067212, 22763276577, -4942614024, 879923655, -95084190, 13308666, -1285068, 455739, -40854, 5358, 288, 27, -6, 1], 'lmfdb_label': '286650.ba1', 'torsion': [12]}
  • id: 12179278
    {'degree': 16, 'field': [10061336585521, 0, 0, 0, -53694047264, 0, 0, 0, 71202066, 0, 0, 0, 4576, 0, 0, 0, 1], 'lmfdb_label': '286650.ba1', 'torsion': [4, 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: 7099108
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '286650.ba1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7099109
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '286650.ba1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7099110
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '286650.ba1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 7099111
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '286650.ba1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7099112
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '286650.ba1', 'prime': 13, 'reduction_type': -1, '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: 3470633
    {'adelic_gens': [[2183, 5712, 6132, 1007], [1, 0, 8, 1], [10913, 8, 10912, 9], [7279, 0, 0, 10919], [1, 8, 0, 1], [1, 4, 4, 17], [3119, 0, 0, 10919], [7, 6, 10914, 10915], [8128, 4683, 10605, 8842], [5923, 7476, 10122, 4621], [8128, 1113, 4347, 694]], 'adelic_image': '10920.48.0.?', 'conductor': 286650, 'lmfdb_label': '286650.ba1', 'prime': 0}
  • id: 1016580
    {'conductor': 286650, 'elladic_image': '4.6.0.1', 'lmfdb_label': '286650.ba1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 286650.ba does not appear in ec_padic