Elliptic curve data - 2178.a2

Formats: - HTML - YAML - JSON - 2024-05-21T04:16:11.968044

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '2178a', 'Clabel': '2178a2', 'Cnumber': 2, 'abc_quality': 1.0492563620983195, 'absD': 370412146368, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 132, 'ainvs': [1, -1, 0, -123987, -16773003], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 2178, 'degree': 7680, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4790066722874728872675048357', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4406910829875, 7744], 'lmfdb_iso': '2178.a', 'lmfdb_label': '2178.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -9222, -338572], 'min_quad_twist_disc': 33, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.48.0-12.h.1.4', '33.8.0-3.a.1.2', '44.6.0.e.1', '66.24.0-6.a.1.2', '132.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.0054059637212601923877217374848', 'prec': 110}, 'szpiro_ratio': 6.088526591399735, '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, -2, -1, 0, 0, 0, 0, -2, 2, 0, 1, 6, 0, -2, 0], 'aplist': [-1, 0, 0, -2, 0, -2, 6, -2, 0, 6, -4, 2, -6, 10, 12, -12, 12, 10, 8, 12, -14, -2, 12, 0, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 2178, 'isogeny_matrix': [[1, 3, 2, 6], [3, 1, 6, 2], [2, 6, 1, 3], [6, 2, 3, 1]], 'lmfdb_iso': '2178.a', 'trace_hash': 2239145659156153101}
• 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': '0.051921965832844598942173391914', 'prec': 107}, 'conductor': 2178, 'gens': [], 'heights': [], 'lmfdb_label': '2178.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.25442243119112323433409711789', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0176897247644929373363884715546408193', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-813, 813, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': 'a', '11': 'a'}, 'iwp0': 5, 'lmfdb_label': '2178.a2'}
• ec_torsion_growth •

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

  
  
  • id: 110564
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '2178.a2', 'torsion': [2, 2]}
  • id: 110565
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '2178.a2', 'torsion': [6]}
  • id: 110566
    {'degree': 4, 'field': [16, -4, 0, -1, 1], 'lmfdb_label': '2178.a2', 'torsion': [4]}
  • id: 110567
    {'degree': 4, 'field': [33, 0, 1, -2, 1], 'lmfdb_label': '2178.a2', 'torsion': [2, 6]}
  • id: 110568
    {'degree': 6, 'field': [-297, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '2178.a2', 'torsion': [6]}
  • id: 110569
    {'degree': 8, 'field': [4, -16, -40, -16, -14, -20, -4, -2, 1], 'lmfdb_label': '2178.a2', 'torsion': [2, 4]}
  • id: 110571
    {'degree': 8, 'field': [16, -24, 20, -12, 6, -6, 5, -3, 1], 'lmfdb_label': '2178.a2', 'torsion': [12]}
  • id: 110570
    {'degree': 8, 'field': [16, 0, 4, 0, 0, 0, 1, 0, 1], 'lmfdb_label': '2178.a2', 'torsion': [2, 4]}
  • id: 110572
    {'degree': 12, 'field': [144, -72, -144, 390, -75, -192, 163, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '2178.a2', 'torsion': [3, 6]}
  • id: 110573
    {'degree': 12, 'field': [4096, 0, -6144, 0, 3840, 0, -1291, 0, 240, 0, -24, 0, 1], 'lmfdb_label': '2178.a2', 'torsion': [2, 6]}
  • id: 110574
    {'degree': 12, 'field': [7744, 0, 0, -968, 0, 0, 132, 0, 0, -11, 0, 0, 1], 'lmfdb_label': '2178.a2', 'torsion': [12]}
  • id: 110576
    {'degree': 16, 'field': [16, 96, 240, 0, -104, 96, 516, -600, 369, 90, -210, 150, -26, -18, 18, -6, 1], 'lmfdb_label': '2178.a2', 'torsion': [2, 12]}
  • id: 110577
    {'degree': 16, 'field': [256, 0, -64, 0, 16, 0, 32, 0, -20, 0, 8, 0, 1, 0, -1, 0, 1], 'lmfdb_label': '2178.a2', 'torsion': [2, 12]}
  • id: 110575
    {'degree': 16, 'field': [256, 0, 1888, 0, 4988, 0, 802, 0, -191, 0, -124, 0, -10, 0, 2, 0, 1], 'lmfdb_label': '2178.a2', 'torsion': [8]}
  • id: 110578
    {'degree': 18, 'field': [785964, -3157236, 6336252, -8330100, 8081154, -6171354, 3895947, -2118342, 1018185, -435362, 164802, -55470, 16863, -4548, 1002, -168, 27, -6, 1], 'lmfdb_label': '2178.a2', 'torsion': [18]}
• 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: 36365
    {'conductor': 2178, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '2178.a2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 36366
    {'conductor': 2178, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '2178.a2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 36367
    {'conductor': 2178, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '2178.a2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1678139
    {'adelic_gens': [[1, 12, 0, 1], [121, 12, 120, 13], [119, 120, 54, 59], [78, 1, 77, 122], [1, 6, 6, 37], [1, 0, 12, 1], [56, 11, 9, 100], [11, 2, 82, 123]], 'adelic_image': '132.96.1.?', 'conductor': 2178, 'lmfdb_label': '2178.a2', 'prime': 0}
  • id: 10702
    {'conductor': 2178, 'elladic_image': '2.3.0.1', 'lmfdb_label': '2178.a2', 'modell_image': '2B', 'prime': 2}
  • id: 10703
    {'conductor': 2178, 'elladic_image': '3.4.0.1', 'lmfdb_label': '2178.a2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 2178.a does not appear in ec_padic