Elliptic curve data - 214.a1

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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': '214b', 'Clabel': '214b1', 'Cnumber': 1, 'abc_quality': 0.8315075692937541, 'absD': 214, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 856, 'ainvs': [1, 0, 1, 1, 0], 'analytic_rank': 1, 'bad_primes': [2, 107], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 214, 'degree': 12, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.86353660306236198978787405708', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [357911, 214], 'lmfdb_iso': '214.a', 'lmfdb_label': '214.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 1, 0], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['856.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.26044902853408521811433827675', 'prec': 103}, 'semistable': True, 'serre_invariants': [[2, 4, 107], [107, 108, 2]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.86353660306236198978787405708', 'prec': 107}, 'szpiro_ratio': 2.38317122464288, '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, -1, -2, 1, -1, 2, 4, -1, 1, 1, -6, -2, -4, -4, 2, 1, -6, -1, -2, -1], 'aplist': [-1, -2, -1, 4, -6, -4, -6, -2, 5, 0, -2, 0, -11, -9, 11, 10, -3, -8, 5, 0, 8, 11, 4, -15, -12], 'class_deg': 1, 'class_size': 1, 'conductor': 214, 'isogeny_matrix': [[1]], 'lmfdb_iso': '214.a', 'trace_hash': 786804783105072942}
• 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': '5.6241690128299514023877203272', 'prec': 100}, 'conductor': 214, 'gens': [[0, 0, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.26044902853408521811433827675', 'prec': 103}], 'lmfdb_label': '214.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '3.4346780132399337533924115785', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.89455855187572263270921736838884598109', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': [0, 2, 672]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [1, 0], '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 1, 0], '41': [1, 0], '43': [3, 0], '47': [1, 0], '107': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '214.a1'}
• ec_torsion_growth •

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

  
  
  • id: 9189
    {'degree': 3, 'field': [11, 1, -1, 1], 'lmfdb_label': '214.a1', 'torsion': [2]}
  • id: 9190
    {'degree': 6, 'field': [144, -48, 194, 28, -3, -2, 1], 'lmfdb_label': '214.a1', 'torsion': [2, 2]}
  • id: 9191
    {'degree': 8, 'field': [-48, 45, -66, 41, -17, -7, 7, -4, 1], 'lmfdb_label': '214.a1', 'torsion': [3]}
  • id: 9192
    {'degree': 12, 'field': [1238, -218, -3225, 4164, -1483, -458, -113, 248, 59, -6, -11, 0, 1], 'lmfdb_label': '214.a1', 'torsion': [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: 1896
    {'conductor': 214, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '214.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1897
    {'conductor': 214, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '214.a1', 'prime': 107, '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

  
  {'adelic_gens': [[429, 2, 429, 3], [215, 2, 0, 1], [1, 0, 2, 1], [1, 2, 0, 1], [537, 2, 537, 3], [855, 2, 854, 3], [1, 1, 855, 0]], 'adelic_image': '856.2.0.?', 'conductor': 214, 'lmfdb_label': '214.a1', 'prime': 0}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 1711
    {'lmfdb_iso': '214.a', 'p': 5, 'prec': 20, 'unit': 431562515719, 'val': 3}
  • id: 1712
    {'lmfdb_iso': '214.a', 'p': 7, 'prec': 20, 'unit': 3434324114945156, 'val': 1}
  • id: 1717
    {'lmfdb_iso': '214.a', 'p': 11, 'prec': 20, 'unit': 37601688604254669929, 'val': 1}
  • id: 1715
    {'lmfdb_iso': '214.a', 'p': 13, 'prec': 20, 'unit': 103409067389698287338, 'val': 2}
  • id: 1718
    {'lmfdb_iso': '214.a', 'p': 17, 'prec': 20, 'unit': 70937781465970769719786, 'val': 1}
  • id: 1719
    {'lmfdb_iso': '214.a', 'p': 19, 'prec': 20, 'unit': 1714061328880767525864529, 'val': 1}
  • id: 1723
    {'lmfdb_iso': '214.a', 'p': 23, 'prec': 20, 'unit': 50880824045961965473992797, 'val': 1}
  • id: 1727
    {'lmfdb_iso': '214.a', 'p': 31, 'prec': 20, 'unit': 12272266135827350896410777999, 'val': 1}
  • id: 1713
    {'lmfdb_iso': '214.a', 'p': 41, 'prec': 20, 'unit': 942155150995553538525145543873, 'val': 1}
  • id: 1714
    {'lmfdb_iso': '214.a', 'p': 43, 'prec': 20, 'unit': 72720335508252521324707075592, 'val': 2}
  • id: 1725
    {'lmfdb_iso': '214.a', 'p': 47, 'prec': 20, 'unit': 33192490205215924570032670453294, 'val': 1}
  • id: 1720
    {'lmfdb_iso': '214.a', 'p': 53, 'prec': 20, 'unit': 309823111784417647440632326102387, 'val': 1}
  • id: 1721
    {'lmfdb_iso': '214.a', 'p': 59, 'prec': 20, 'unit': 451881411949108673234662527430132, 'val': 1}
  • id: 1726
    {'lmfdb_iso': '214.a', 'p': 61, 'prec': 20, 'unit': 3470902029463984180423264922890802, 'val': 1}
  • id: 1710
    {'lmfdb_iso': '214.a', 'p': 67, 'prec': 20, 'unit': 31421707826999958400131554739867320, 'val': 1}
  • id: 1722
    {'lmfdb_iso': '214.a', 'p': 73, 'prec': 20, 'unit': 202559049002233617838543529663580262, 'val': 1}
  • id: 1716
    {'lmfdb_iso': '214.a', 'p': 79, 'prec': 20, 'unit': 674077750528420036423959942369832805, 'val': 1}
  • id: 1709
    {'lmfdb_iso': '214.a', 'p': 83, 'prec': 20, 'unit': 2271462287857717318220073636265712013, 'val': 1}
  • id: 1724
    {'lmfdb_iso': '214.a', 'p': 89, 'prec': 20, 'unit': 65824029423769096078308933882799425, 'val': 1}
  • id: 1708
    {'lmfdb_iso': '214.a', 'p': 97, 'prec': 20, 'unit': 49010961362052092500285565234594638086, 'val': 1}