Elliptic curve data - 214896.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
  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': '214896t', 'Clabel': '214896t2', 'Cnumber': 2, 'abc_quality': 1.0039533759828516, 'absD': 806055985152, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4884, 'ainvs': [0, -1, 0, -101240, -12364944], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 214896, 'degree': 1216512, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4639396546585444333824495669', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [21049724100131, 147852], 'lmfdb_iso': '214896.b', 'lmfdb_label': '214896.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -6328, 193202], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '66.6.0.a.1', '444.6.0.?', '1628.6.0.?', '4884.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 33], [3, 4, 71632], [11, 42, 1776], [37, 38, 5808]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.17131865589900648794973155095', 'prec': 103}, 'szpiro_ratio': 3.761989015334005, '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, 0, -1, 0, -4, 0, 2, 0, 1, 0, 0, 0, -2, 0, 4, 0, 2, 0, 8, 0], 'aplist': [0, -1, -4, 2, 0, -2, 2, 8, 6, 6, 4, -1, -6, -4, 4, -14, -6, -2, -4, 16, -12, -8, -12, 0, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 214896, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '214896.b', 'trace_hash': 114641511753217478}
• 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': '0.053510396903433569524475294684', 'prec': 107}, 'conductor': 214896, 'gens': [], 'heights': [], 'lmfdb_label': '214896.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.26764636293779275202263384399', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0705854517511710080905353759645871735', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-183, 0, 1]], 'xcoord_integral_points': [-183]}
• lmfdb_label 214896.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9375638
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '214896.b1', 'torsion': [2, 2]}
  • id: 9375639
    {'degree': 4, 'field': [603, -28, 29, -2, 1], 'lmfdb_label': '214896.b1', 'torsion': [4]}
  • id: 9375642
    {'degree': 8, 'field': [-3267, 0, 4356, 0, 198, 0, 0, 0, 1], 'lmfdb_label': '214896.b1', 'torsion': [6]}
  • id: 9375641
    {'degree': 8, 'field': [144, 0, -4176, 0, 633, 0, -84, 0, 1], 'lmfdb_label': '214896.b1', 'torsion': [2, 4]}
  • id: 9375640
    {'degree': 8, 'field': [6561, 0, 243, 0, 1080, 0, 3, 0, 1], 'lmfdb_label': '214896.b1', 'torsion': [2, 4]}
  • id: 9375644
    {'degree': 16, 'field': [891136, 122720, -642718, -751798, 121341, 397250, 79438, -89636, 10167, 8044, -2986, 218, -133, 42, 14, -8, 1], 'lmfdb_label': '214896.b1', 'torsion': [2, 6]}
  • id: 9375643
    {'degree': 16, 'field': [231699288496, 17524801264, 35973854476, 1293218804, 2298928821, -6418056, 155475044, -30063444, 13214908, -1976484, 477470, -42576, 8520, -412, 100, -8, 1], 'lmfdb_label': '214896.b1', 'torsion': [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: 5327280
    {'conductor': 214896, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '214896.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5327281
    {'conductor': 214896, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '214896.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5327282
    {'conductor': 214896, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '214896.b1', 'prime': 11, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5327283
    {'conductor': 214896, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '214896.b1', 'prime': 37, 'reduction_type': -1, '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: 3037735
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1630, 1, 1627, 0], [1, 4, 0, 1], [3665, 1222, 1220, 3663], [4881, 4, 4880, 5], [448, 1, 3551, 0], [3961, 4, 3038, 9]], 'adelic_image': '4884.12.0.?', 'conductor': 214896, 'lmfdb_label': '214896.b1', 'prime': 0}
  • id: 790846
    {'conductor': 214896, 'elladic_image': '2.3.0.1', 'lmfdb_label': '214896.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 214896.b does not appear in ec_padic