Elliptic curve data - 8450.b2

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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': '8450i', 'Clabel': '8450i1', 'Cnumber': 1, 'abc_quality': 0.9455380306483595, 'absD': 1325562421625000000, 'adelic_genus': 5, 'adelic_index': 144, 'adelic_level': 1560, 'ainvs': [1, 0, 1, -289501, -22961352], 'analytic_rank': 0, 'bad_primes': [2, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 8450, 'degree': 134784, 'elladic_images': ['2.3.0.1', '3.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1704642584644924884879057813', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [16194277, 8000], 'lmfdb_iso': '8450.b', 'lmfdb_label': '8450.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -68, -112], 'min_quad_twist_disc': 65, 'modell_images': ['2B', '3Ns'], 'modm_images': ['2.3.0.a.1', '3.6.0.b.1', '6.18.0.b.1', '24.36.0.d.1', '30.36.0.d.1', '39.12.0.a.1', '40.6.0.f.1', '78.36.0.?', '104.6.0.?', '120.72.1.?', '130.6.0.?', '312.72.1.?', '390.72.1.?', '520.12.0.?', '1560.144.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 325], [3, 2, 4225], [5, 18, 338], [13, 62, 50]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.55796671584871025085258946648', 'prec': 107}, 'szpiro_ratio': 5.45695281202063, '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, -2, 1, 0, 2, 0, -1, 1, 0, 0, -2, 0, 0, 0, 1, -6, -1, 0, 0], 'aplist': [-1, -2, 0, 0, 0, 0, -6, 0, 0, 6, -6, -6, 0, -10, 12, 0, -12, 10, -12, 6, 6, -8, 12, -12, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 8450, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '8450.b', 'trace_hash': 2154208694942743729}
• 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': '0.013024429184246980893945234692', 'prec': 107}, 'conductor': 8450, 'gens': [], 'heights': [], 'lmfdb_label': '8450.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.21650421619166013511529451009', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.43300843238332027023058902018350216482', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-493, 246, 1]], 'xcoord_integral_points': [-493]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '5': 'a', '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '8450.b2'}
• ec_torsion_growth •

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

  
  
  • id: 442275
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '8450.b2', 'torsion': [2, 2]}
  • id: 442277
    {'degree': 4, 'field': [-36, -48, 15, -1, 1], 'lmfdb_label': '8450.b2', 'torsion': [6]}
  • id: 442278
    {'degree': 4, 'field': [120, 30, -11, -1, 1], 'lmfdb_label': '8450.b2', 'torsion': [6]}
  • id: 442276
    {'degree': 4, 'field': [143, -52, 0, 0, 1], 'lmfdb_label': '8450.b2', 'torsion': [4]}
  • id: 442282
    {'degree': 8, 'field': [-36, -114, 13, 68, -12, 18, 0, -2, 1], 'lmfdb_label': '8450.b2', 'torsion': [2, 6]}
  • id: 442283
    {'degree': 8, 'field': [16, -24, 0, -54, 131, -27, 0, -3, 1], 'lmfdb_label': '8450.b2', 'torsion': [2, 6]}
  • id: 442279
    {'degree': 8, 'field': [16, 0, -72, 0, 24, 0, -18, 0, 1], 'lmfdb_label': '8450.b2', 'torsion': [2, 4]}
  • id: 442280
    {'degree': 8, 'field': [196, 0, 186, 0, 97, 0, 4, 0, 1], 'lmfdb_label': '8450.b2', 'torsion': [2, 4]}
  • id: 442281
    {'degree': 8, 'field': [4356, 0, -2505, 0, 487, 0, -35, 0, 1], 'lmfdb_label': '8450.b2', 'torsion': [3, 6]}
  • id: 442285
    {'degree': 16, 'field': [2304, 4608, 912, -6216, -2768, 2382, 609, 656, 614, -1000, 245, -82, 33, 6, 2, -2, 1], 'lmfdb_label': '8450.b2', 'torsion': [6, 6]}
  • id: 442286
    {'degree': 16, 'field': [42524, -54808, 41114, -74964, 80539, -44444, 23878, -27360, 26630, -14580, 5052, -832, 130, -20, 20, -4, 1], 'lmfdb_label': '8450.b2', 'torsion': [12]}
  • id: 442287
    {'degree': 16, 'field': [1578775, 651680, -189426, -786328, 66370, 341572, -34498, -58248, 2683, 7164, -258, -1192, 684, -252, 56, -8, 1], 'lmfdb_label': '8450.b2', 'torsion': [12]}
  • id: 442284
    {'degree': 16, 'field': [219079844, 258199440, 195791544, 72142848, 23572326, 5378488, 3210164, 799384, 234203, 1436, 5550, 1024, 281, 152, -26, -4, 1], 'lmfdb_label': '8450.b2', '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: 176188
    {'conductor': 8450, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '8450.b2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 176189
    {'conductor': 8450, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '8450.b2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 176190
    {'conductor': 8450, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '8450.b2', 'prime': 13, '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: 1719868
    {'adelic_gens': [[10, 3, 1221, 1552], [781, 12, 0, 1301], [7, 12, 144, 247], [492, 5, 187, 1488], [781, 12, 6, 73], [1, 0, 12, 1], [1, 6, 6, 37], [5, 12, 1512, 1445], [725, 588, 1338, 707], [1, 12, 0, 1], [1549, 12, 1548, 13]], 'adelic_image': '1560.144.5.?', 'conductor': 8450, 'lmfdb_label': '8450.b2', 'prime': 0}
  • id: 41401
    {'conductor': 8450, 'elladic_image': '2.3.0.1', 'lmfdb_label': '8450.b2', 'modell_image': '2B', 'prime': 2}
  • id: 41402
    {'conductor': 8450, 'elladic_image': '3.6.0.1', 'lmfdb_label': '8450.b2', 'modell_image': '3Ns', 'prime': 3}
• lmfdb_iso 8450.b does not appear in ec_padic