Elliptic curve data - 21840.e4

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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': '21840y', 'Clabel': '21840y3', 'Cnumber': 3, 'abc_quality': 1.0195198747653818, 'absD': 13813385564160000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 520, 'ainvs': [0, -1, 0, 59864, 419440], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 21840, 'degree': 147456, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7864702271880005765753374052', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [5792335463322071, 3372408585000], 'lmfdb_iso': '21840.e', 'lmfdb_label': '21840.e4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 3741, -6554], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '40.24.0-40.bb.1.6', '52.12.0-4.c.1.2', '104.24.0.?', '520.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 13], [3, 4, 7280], [5, 6, 4368], [7, 8, 3120], [13, 14, 1680]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0933230466280552671581052837', 'prec': 100}, 'szpiro_ratio': 4.465103852701878, '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, -1, 0, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 2, 0, 8, 0], 'aplist': [0, -1, -1, -1, 0, -1, 2, 8, 4, 6, 8, -6, 2, 12, 0, 10, 8, -2, 4, -8, 6, 0, 4, -6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 21840, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '21840.e', 'trace_hash': 526543172940502764}
• 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': '0.028073184279501653852551370032', 'prec': 107}, 'conductor': 21840, 'gens': [], 'heights': [], 'lmfdb_label': '21840.e4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.23939673674611549621639632733', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9151738939689239697311706186180718981', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-7, 0, 1]], 'xcoord_integral_points': [-7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '7': [0, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '21840.e4'}
• ec_torsion_growth •

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

  
  
  • id: 1109436
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '21840.e4', 'torsion': [4]}
  • id: 1109437
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [4]}
  • id: 1109435
    {'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [2, 2]}
  • id: 1109438
    {'degree': 4, 'field': [27, 2, -1, -2, 1], 'lmfdb_label': '21840.e4', 'torsion': [2, 4]}
  • id: 1109442
    {'degree': 8, 'field': [-48, 0, 181, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [6]}
  • id: 1109441
    {'degree': 8, 'field': [1521, 0, -572, 0, 108, 0, -12, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [8]}
  • id: 1109440
    {'degree': 8, 'field': [54756, 0, -36504, 0, -2223, 0, 39, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [8]}
  • id: 1109439
    {'degree': 8, 'field': [56644, 0, 5584, 0, 492, 0, -8, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [2, 4]}
  • id: 1109445
    {'degree': 16, 'field': [6561, 0, -15228, 0, 51156, 0, -57848, 0, 28439, 0, -4328, 0, 436, 0, -28, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [2, 8]}
  • id: 1109447
    {'degree': 16, 'field': [203844, -158844, 40862, 349742, -429235, 222544, 59242, -106184, 17634, 4086, 714, -440, -230, 112, 4, -8, 1], 'lmfdb_label': '21840.e4', 'torsion': [12]}
  • id: 1109448
    {'degree': 16, 'field': [240100, 0, 240100, 0, 60025, 0, -6432, 0, -4548, 0, 1002, 0, 64, 0, 16, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [12]}
  • id: 1109444
    {'degree': 16, 'field': [153784801, 0, 236738960, 0, 50453573, 0, 932256, 0, 42164, 0, 38064, 0, -1819, 0, -16, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [2, 8]}
  • id: 1109443
    {'degree': 16, 'field': [187388721, 0, 0, 0, 0, 0, 0, 0, 465426, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [4, 4]}
  • id: 1109446
    {'degree': 16, 'field': [190094256004, 0, 67640561812, 0, 9109212025, 0, 685674336, 0, 32418060, 0, 987114, 0, 18880, 0, 208, 0, 1], 'lmfdb_label': '21840.e4', 'torsion': [2, 6]}
• 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: 497994
    {'conductor': 21840, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '21840.e4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 497995
    {'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21840.e4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 497996
    {'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '21840.e4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 497997
    {'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '21840.e4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 497998
    {'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21840.e4', '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: 1810143
    {'adelic_gens': [[513, 8, 512, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [164, 1, 423, 6], [417, 8, 108, 33], [456, 203, 329, 358], [192, 447, 167, 120], [7, 6, 514, 515]], 'adelic_image': '520.48.0.?', 'conductor': 21840, 'lmfdb_label': '21840.e4', 'prime': 0}
  • id: 101056
    {'conductor': 21840, 'elladic_image': '8.12.0.7', 'lmfdb_label': '21840.e4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 21840.e does not appear in ec_padic