Elliptic curve data - 229320.i4

Formats: - HTML - YAML - JSON - 2025-10-15T09:11:54.134224

• 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': '229320bf', 'Clabel': '229320bf3', 'Cnumber': 3, 'abc_quality': 1.0213953201021033, 'absD': 1337951487600000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2184, 'ainvs': [0, 0, 0, 275037, 3853262], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 229320, 'degree': 3538944, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1675814440737389919319196983', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2, 4], 'jinv': [26198797244, 15234375], 'lmfdb_iso': '229320.i', 'lmfdb_label': '229320.i4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 624, 624], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '28.12.0-4.c.1.1', '78.6.0.?', '104.12.0.?', '156.12.0.?', '168.24.0.?', '312.24.0.?', '728.24.0.?', '1092.24.0.?', '2184.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '9.6120350749891700985724521562', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 5733], [3, 8, 25480], [5, 6, 45864], [7, 26, 4680], [13, 14, 17640]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.067697574745406402500593940232', 'prec': 107}, 'szpiro_ratio': 3.9850999871771764, '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, 0, 0, 0, -1, 0, 0, 0, 0, 0, -4, 0, -1, 0, 0, 0, -6, 0, 0, 0], 'aplist': [0, 0, -1, 0, -4, -1, -6, 0, 8, -6, 4, -2, -10, -4, -8, 2, 12, 2, -16, 8, 6, -16, 4, -2, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 229320, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '229320.i', 'trace_hash': 930359859226571086}
• 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': '0.013099740106799014555450728815', 'prec': 107}, 'conductor': 229320, 'gens': [[611, 20000, 1], [67, 4752, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.6072841102448830933600501679', 'prec': 100}, {'__RealLiteral__': 0, 'data': '4.1957298490888492162827916931', 'prec': 100}], 'lmfdb_label': '229320.i4', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.16334920484747761682352450709', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.560946291724366579186889153950840985', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-14, 0, 1]], 'xcoord_integral_points': [-14, 67, 182, 427, 611]}
• lmfdb_label 229320.i4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9947911
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '229320.i4', 'torsion': [4]}
  • id: 9947910
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '229320.i4', 'torsion': [2, 2]}
  • id: 9947912
    {'degree': 2, 'field': [273, 0, 1], 'lmfdb_label': '229320.i4', 'torsion': [4]}
  • id: 9947913
    {'degree': 4, 'field': [282, -6, 7, -2, 1], 'lmfdb_label': '229320.i4', 'torsion': [2, 4]}
  • id: 9947917
    {'degree': 8, 'field': [-3790302, -1488984, 35862, 94194, 10836, -612, -166, -4, 1], 'lmfdb_label': '229320.i4', 'torsion': [6]}
  • id: 9947915
    {'degree': 8, 'field': [-111, 78, 96, -90, 25, 2, 0, -4, 1], 'lmfdb_label': '229320.i4', 'torsion': [8]}
  • id: 9947916
    {'degree': 8, 'field': [690561, 0, 135792, 0, 1918, 0, 32, 0, 1], 'lmfdb_label': '229320.i4', 'torsion': [8]}
  • id: 9947914
    {'degree': 8, 'field': [1972636, 28048, -25216, -5672, 2857, -28, 14, -4, 1], 'lmfdb_label': '229320.i4', 'torsion': [2, 4]}
  • id: 9947922
    {'degree': 16, 'field': [-903435804, 388538496, 339369480, -105707424, -50544372, -15821352, 5503112, 2218448, -654108, 88672, 32688, -17784, 1048, 684, -84, -4, 1], 'lmfdb_label': '229320.i4', 'torsion': [12]}
  • id: 9947920
    {'degree': 16, 'field': [42025, 0, -54732, 0, 45562, 0, -2868, 0, -3333, 0, 564, 0, 106, 0, 0, 0, 1], 'lmfdb_label': '229320.i4', 'torsion': [2, 8]}
  • id: 9947919
    {'degree': 16, 'field': [476243329, 0, 326342976, 0, 93747046, 0, 3059388, 0, 2028327, 0, 189828, 0, 7198, 0, 132, 0, 1], 'lmfdb_label': '229320.i4', 'torsion': [2, 8]}
  • id: 9947918
    {'degree': 16, 'field': [15096053956, 0, -1516565064, 0, -100822928, 0, 7096212, 0, 869685, 0, -4464, 0, -1334, 0, -12, 0, 1], 'lmfdb_label': '229320.i4', 'torsion': [4, 4]}
  • id: 9947921
    {'degree': 16, 'field': [19591288258000, -8598233847040, 240307167072, 1066135243008, -38920639272, -47395637832, 1357836364, 860663576, -59884167, -3783804, 1918524, -67968, -26974, 904, 72, -4, 1], 'lmfdb_label': '229320.i4', 'torsion': [2, 6]}
  • id: 9947923
    {'degree': 16, 'field': [44603136959364, 0, 407174610888, 0, 71439284700, 0, -626036904, 0, 85213080, 0, 138864, 0, -9972, 0, 0, 0, 1], 'lmfdb_label': '229320.i4', 'torsion': [12]}
• 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: 5686603
    {'conductor': 229320, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '229320.i4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5686604
    {'conductor': 229320, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '229320.i4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5686605
    {'conductor': 229320, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '229320.i4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5686606
    {'conductor': 229320, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '229320.i4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5686607
    {'conductor': 229320, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '229320.i4', 'prime': 13, '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

  
  
  • id: 3126199
    {'adelic_gens': [[2177, 8, 2176, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [43, 1288, 1778, 981], [43, 42, 2002, 1219], [7, 6, 2178, 2179], [1828, 1561, 1463, 1254], [1448, 1869, 203, 622], [935, 0, 0, 2183]], 'adelic_image': '2184.48.0.?', 'conductor': 229320, 'lmfdb_label': '229320.i4', 'prime': 0}
  • id: 836869
    {'conductor': 229320, 'elladic_image': '4.6.0.1', 'lmfdb_label': '229320.i4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 229320.i does not appear in ec_padic