Elliptic curve data - 212415.bi1

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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': '212415bm', 'Clabel': '212415bm2', 'Cnumber': 2, 'abc_quality': 1.1355694477957907, 'absD': 1554529555564453125, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 210, 'ainvs': [0, -1, 1, -11687545, 15382955181], 'analytic_rank': 2, 'bad_primes': [3, 5, 7, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 212415, 'degree': 7464960, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6571889299474257716219113431', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 34, 'isogeny_degrees': [1, 3], 'jinv': [17968412610002944, 158203125], 'lmfdb_iso': '212415.bi', 'lmfdb_label': '212415.bi1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -238521, -44916415], 'min_quad_twist_disc': -7, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '10.2.0.a.1', '21.8.0-3.a.1.2', '30.8.0.a.1', '210.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 18, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.40054418192937221640397100597', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 70805], [3, 4, 14161], [5, 6, 42483], [7, 26, 4335], [17, 114, 735]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.73982940740103042565272343209', 'prec': 103}, 'szpiro_ratio': 4.926972264233907, '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, 0, -1, -2, 1, 0, 0, 0, 1, 0, -3, 2, 4, 0, -1, 4, 0, 0, -5, -2], 'aplist': [0, -1, 1, 0, -3, 4, 0, -5, 0, -3, -8, 2, 3, -10, 6, -6, -15, -5, 2, -15, -2, -1, 6, -9, 10], 'class_deg': 3, 'class_size': 2, 'conductor': 212415, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '212415.bi', 'trace_hash': 1278896543540862305}
• 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': '0.0049203389435032331098750991386', 'prec': 110}, 'conductor': 212415, 'gens': [[1315, 47812, 1], [9085, 187421, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '0.59632630592617354063305234605', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.68877017664086751809561706398', 'prec': 103}], 'lmfdb_label': '212415.bi1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.24103829963967993095410426079', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.427020762624829116616382811779981040', 'prec': 130}, 'tamagawa_product': 108, 'torsion_generators': [], 'xcoord_integral_points': [-2935, 1315, 1855, 1927, 1965, 1995, 3815, 3925, 9282565]}
• lmfdb_label 212415.bi1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9277384
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '212415.bi1', 'torsion': [3]}
  • id: 9277385
    {'degree': 3, 'field': [5, -11, -1, 1], 'lmfdb_label': '212415.bi1', 'torsion': [2]}
  • id: 9277388
    {'degree': 6, 'field': [-185, -81, 206, 23, -38, -1, 1], 'lmfdb_label': '212415.bi1', 'torsion': [6]}
  • id: 9277386
    {'degree': 6, 'field': [-125, -25, 130, 15, -26, -1, 1], 'lmfdb_label': '212415.bi1', 'torsion': [2, 2]}
  • id: 9277387
    {'degree': 6, 'field': [2864, -471, -135, 89, 9, -3, 1], 'lmfdb_label': '212415.bi1', 'torsion': [3]}
  • id: 9277389
    {'degree': 12, 'field': [-8868410, 27887796, -21830260, -2032324, 3175018, -133856, -155480, 11456, 2866, -2, -46, -6, 1], 'lmfdb_label': '212415.bi1', 'torsion': [4]}
  • id: 9277391
    {'degree': 12, 'field': [-4500, 28800, -22380, -90900, 42736, 40546, -15107, -5672, 1779, 278, -77, -4, 1], 'lmfdb_label': '212415.bi1', 'torsion': [2, 6]}
  • id: 9277390
    {'degree': 12, 'field': [5541316, 1052238, -202725, 617857, 59460, -34773, 17735, 438, -435, 203, 0, -3, 1], 'lmfdb_label': '212415.bi1', 'torsion': [3, 3]}
  • id: 9277393
    {'degree': 18, 'field': [528284, 3504420, 5763834, 8138607, 24871635, -41413248, 40411974, -25709715, 13284009, -4875133, 1360503, -236043, 14397, 12411, -2691, 234, 54, -9, 1], 'lmfdb_label': '212415.bi1', 'torsion': [6]}
  • id: 9277392
    {'degree': 18, 'field': [2091051, 5085720, 6752808, 5584635, 4442904, 2747520, 2009988, 1238400, 597888, 292155, 112464, 41040, 13300, 2280, 144, -125, -48, 0, 1], 'lmfdb_label': '212415.bi1', '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: 5265595
    {'conductor': 212415, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '212415.bi1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5265596
    {'conductor': 212415, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '212415.bi1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 5265597
    {'conductor': 212415, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '212415.bi1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5265598
    {'conductor': 212415, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '212415.bi1', 'prime': 17, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 3022691
    {'adelic_gens': [[127, 126, 21, 169], [1, 0, 6, 1], [4, 3, 9, 7], [3, 4, 8, 11], [8, 147, 175, 127], [179, 0, 0, 209], [1, 6, 0, 1], [205, 6, 204, 7]], 'adelic_image': '210.16.0.?', 'conductor': 212415, 'lmfdb_label': '212415.bi1', 'prime': 0}
  • id: 782914
    {'conductor': 212415, 'elladic_image': '3.4.0.1', 'lmfdb_label': '212415.bi1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 212415.bi does not appear in ec_padic