Elliptic curve data - 19166.a4

Formats: - HTML - YAML - JSON - 2026-07-11T14:46:11.030770

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '19166a', 'Clabel': '19166a2', 'Cnumber': 2, 'abc_quality': 0.9676277689392396, 'absD': 251441188082, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 18648, 'ainvs': [1, 0, 0, -14403, 663679], 'analytic_rank': 1, 'bad_primes': [2, 7, 37], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 19166, 'degree': 34560, 'elladic_images': ['8.6.0.6', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1199476480770869883695849534', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [128787625, 98], 'lmfdb_iso': '19166.a', 'lmfdb_label': '19166.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -11, 12], 'min_quad_twist_disc': 37, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.b.1', '9.12.0.a.1', '18.36.0.a.1', '24.24.0.y.1', '28.6.0.c.1', '56.12.0.k.1', '63.36.0.d.2', '72.72.1.?', '84.24.0.?', '111.8.0.?', '126.108.2.?', '168.48.1.?', '222.24.0.?', '252.216.7.?', '333.24.0.?', '504.432.21.?', '666.72.0.?', '888.48.0.?', '2331.72.0.?', '2664.144.1.?', '3108.48.0.?', '4662.216.2.?', '6216.96.1.?', '9324.432.7.?', '18648.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.6341391709079743635462328207', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1369], [7, 8, 2738], [37, 686, 14]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.68551130824502523381446288212', 'prec': 107}, 'szpiro_ratio': 4.090824444602284, '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, 1, 1, 1, 0, 0, -2, 4, 1, 0, 1, -6, 1, -2, 0], 'aplist': [1, -2, 0, 1, 0, 4, -6, -2, 0, 6, 4, 0, 6, -8, -12, 6, 6, -8, -4, 0, 2, -8, -6, 6, 10], 'class_deg': 18, 'class_size': 6, 'conductor': 19166, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '19166.a', 'trace_hash': 108263830858770119}
• 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': '0.10646965157764930485802114739', 'prec': 103}, 'conductor': 19166, 'gens': [[-429, 8339, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '5.6341391709079743635462328207', 'prec': 100}], 'lmfdb_label': '19166.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.97719183324903394805125769388', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5056347851997556642322042115900514463', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[271, -271, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [7, 0], '5': [1, 3, 0], '7': [2, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': 'a', '41': [1, 0], '43': [3, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '19166.a4'}
• ec_torsion_growth •

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

  
  
  • id: 980855
    {'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '19166.a4', 'torsion': [6]}
  • id: 980854
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '19166.a4', 'torsion': [2, 2]}
  • id: 980857
    {'degree': 4, 'field': [47, 22, -21, -2, 1], 'lmfdb_label': '19166.a4', 'torsion': [2, 6]}
  • id: 980856
    {'degree': 4, 'field': [2738, 0, -37, 0, 1], 'lmfdb_label': '19166.a4', 'torsion': [4]}
  • id: 980859
    {'degree': 6, 'field': [-433, -100, 257, 21, -32, -1, 1], 'lmfdb_label': '19166.a4', 'torsion': [18]}
  • id: 980858
    {'degree': 6, 'field': [14790, -372, 2350, -67, 93, -1, 1], 'lmfdb_label': '19166.a4', 'torsion': [6]}
  • id: 980862
    {'degree': 8, 'field': [5467, 2534, -2026, -978, 395, 110, -32, -4, 1], 'lmfdb_label': '19166.a4', 'torsion': [12]}
  • id: 980860
    {'degree': 8, 'field': [15376, 0, -3744, 0, -602, 0, -8, 0, 1], 'lmfdb_label': '19166.a4', 'torsion': [2, 4]}
  • id: 980861
    {'degree': 8, 'field': [444889, 0, -32002, 0, 1882, 0, -34, 0, 1], 'lmfdb_label': '19166.a4', 'torsion': [2, 4]}
  • id: 980866
    {'degree': 12, 'field': [-6167, 69468, -143122, -71210, 98983, 22184, -21217, -2650, 1930, 126, -75, -2, 1], 'lmfdb_label': '19166.a4', 'torsion': [2, 18]}
  • id: 980863
    {'degree': 12, 'field': [571536, 0, -402192, 0, 134848, 0, -16381, 0, 1251, 0, -55, 0, 1], 'lmfdb_label': '19166.a4', 'torsion': [3, 6]}
  • id: 980864
    {'degree': 12, 'field': [654724, 84616, -415716, -26034, 111352, 2166, -15763, 0, 1269, -4, -55, 0, 1], 'lmfdb_label': '19166.a4', 'torsion': [18]}
  • id: 980865
    {'degree': 12, 'field': [36000000, 0, -8160000, 0, 746800, 0, -28322, 0, -312, 0, 34, 0, 1], 'lmfdb_label': '19166.a4', 'torsion': [2, 6]}
  • id: 980868
    {'degree': 16, 'field': [2738687, 9651600, -1781228, -12880744, -171164, 6481256, 98304, -1621128, 32929, 215800, -11964, -15456, 1302, 560, -60, -8, 1], 'lmfdb_label': '19166.a4', 'torsion': [2, 12]}
  • id: 980869
    {'degree': 16, 'field': [82064689, 50177204, -34673266, -27895512, 6589752, 7683256, -761754, -1326360, 76261, 148080, -8430, -10360, 756, 420, -40, -8, 1], 'lmfdb_label': '19166.a4', 'torsion': [2, 12]}
  • id: 980867
    {'degree': 16, 'field': [17312243776, 0, -3810895744, 0, 43343506, 0, 16897052, 0, 1955085, 0, 147198, 0, 5676, 0, 114, 0, 1], 'lmfdb_label': '19166.a4', '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: 433140
    {'conductor': 19166, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '19166.a4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 433141
    {'conductor': 19166, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '19166.a4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 433142
    {'conductor': 19166, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '19166.a4', 'prime': 37, '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: 1792142
    {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [4663, 14652, 12358, 15985], [8881, 14652, 2442, 1777], [15652, 15651, 6105, 4330], [10361, 14652, 0, 1], [18613, 36, 18612, 37], [19, 36, 3240, 6139], [4031, 0, 0, 18647], [1, 18, 14, 253]], 'adelic_image': '18648.864.21.?', 'conductor': 19166, 'lmfdb_label': '19166.a4', 'prime': 0}
  • id: 89633
    {'conductor': 19166, 'elladic_image': '8.6.0.6', 'lmfdb_label': '19166.a4', 'modell_image': '2B', 'prime': 2}
  • id: 89634
    {'conductor': 19166, 'elladic_image': '9.12.0.1', 'lmfdb_label': '19166.a4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 886254
    {'lmfdb_iso': '19166.a', 'p': 13, 'prec': 20, 'unit': 819756019544595554790, 'val': 1}
  • id: 886256
    {'lmfdb_iso': '19166.a', 'p': 17, 'prec': 20, 'unit': 155614124291569529590554, 'val': 1}
  • id: 886257
    {'lmfdb_iso': '19166.a', 'p': 19, 'prec': 20, 'unit': 67604982381205454141289, 'val': 2}
  • id: 886253
    {'lmfdb_iso': '19166.a', 'p': 29, 'prec': 20, 'unit': 3879749850552094660288981326, 'val': 1}
  • id: 886264
    {'lmfdb_iso': '19166.a', 'p': 31, 'prec': 20, 'unit': 17622678275850973852887507587, 'val': 1}
  • id: 886251
    {'lmfdb_iso': '19166.a', 'p': 41, 'prec': 20, 'unit': 4054329499237003964497136091554, 'val': 1}
  • id: 886252
    {'lmfdb_iso': '19166.a', 'p': 43, 'prec': 20, 'unit': 9719125592416674301273054031, 'val': 2}
  • id: 886262
    {'lmfdb_iso': '19166.a', 'p': 47, 'prec': 20, 'unit': 11983950675385584129534032194157, 'val': 1}
  • id: 886258
    {'lmfdb_iso': '19166.a', 'p': 53, 'prec': 20, 'unit': 428647967030011709831419967553862, 'val': 1}
  • id: 886259
    {'lmfdb_iso': '19166.a', 'p': 59, 'prec': 20, 'unit': 2180855717997148167253428326110202, 'val': 1}
  • id: 886263
    {'lmfdb_iso': '19166.a', 'p': 61, 'prec': 20, 'unit': 6302725397175612964057333128841535, 'val': 1}
  • id: 886250
    {'lmfdb_iso': '19166.a', 'p': 67, 'prec': 20, 'unit': 35900161851990162566775427547788984, 'val': 1}
  • id: 886260
    {'lmfdb_iso': '19166.a', 'p': 73, 'prec': 20, 'unit': 235296277524263292373552071401924986, 'val': 1}
  • id: 886255
    {'lmfdb_iso': '19166.a', 'p': 79, 'prec': 20, 'unit': 688545865597753074701163751201410223, 'val': 1}
  • id: 886249
    {'lmfdb_iso': '19166.a', 'p': 83, 'prec': 20, 'unit': 379994610206622419088055515998970738, 'val': 1}
  • id: 886261
    {'lmfdb_iso': '19166.a', 'p': 89, 'prec': 20, 'unit': 8937261591818118695723451751882306653, 'val': 1}
  • id: 886248
    {'lmfdb_iso': '19166.a', 'p': 97, 'prec': 20, 'unit': 13812931372219179879083650479051144531, 'val': 1}