Elliptic curve data - 221880.e1

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

  
  {'Ciso': '221880bd', 'Clabel': '221880bd4', 'Cnumber': 4, 'abc_quality': 0.9901572900960728, 'absD': 75152409598863360, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 5160, 'ainvs': [0, -1, 0, -457960936, -3772013079380], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 43], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 221880, 'degree': 31223808, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2925523935437105764461906131', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [820480625548035842, 5805], 'lmfdb_iso': '221880.e', 'lmfdb_label': '221880.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -247680, 47361888], 'min_quad_twist_disc': -43, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '20.12.0-4.c.1.1', '24.12.0.y.1', '120.24.0.?', '344.12.0.?', '1032.24.0.?', '1720.24.0.?', '5160.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 100, 'sha_primes': [2, 5], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.77656742018364616441063991176', 'prec': 103}, 'szpiro_ratio': 5.803502298997408, '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, 0, 0, 1, 0, 4, 0, 2, 0, 1, 0, 6, 0, 4, 0], 'aplist': [0, -1, -1, 0, 4, 2, 6, 4, 8, -6, 0, 10, -6, 0, 8, -2, 4, 14, 4, 16, -10, 8, -16, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 221880, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '221880.e', 'trace_hash': 646084531332982775}
• 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': '0.0013807826718249793759436551975', 'prec': 110}, 'conductor': 221880, 'gens': [], 'heights': [], 'lmfdb_label': '221880.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.032635663459637869942272017206', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '100.00000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2635663459637869942272017205730679119', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-12355, 0, 1]], 'xcoord_integral_points': [-12355]}
• lmfdb_label 221880.e1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9659018
    {'degree': 2, 'field': [-1290, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [2, 2]}
  • id: 9659019
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [4]}
  • id: 9659020
    {'degree': 2, 'field': [258, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [4]}
  • id: 9659021
    {'degree': 4, 'field': [64009, 0, 526, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [2, 4]}
  • id: 9659025
    {'degree': 8, 'field': [-49923, 0, 10836, 0, -774, 0, 0, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [6]}
  • id: 9659022
    {'degree': 8, 'field': [1655071, 20644, -23218, 5152, -2585, 8, 2, -4, 1], 'lmfdb_label': '221880.e1', 'torsion': [2, 4]}
  • id: 9659023
    {'degree': 8, 'field': [3744225, 0, -832050, 0, 52890, 0, 430, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [8]}
  • id: 9659024
    {'degree': 8, 'field': [4696147, 215668, -208834, -13568, 6535, 296, -94, -4, 1], 'lmfdb_label': '221880.e1', 'torsion': [8]}
  • id: 9659029
    {'degree': 16, 'field': [87104889, 0, -118174988556, 0, -9936036180, 0, -65940948, 0, -25475490, 0, 755052, 0, -68, 0, -140, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [2, 6]}
  • id: 9659030
    {'degree': 16, 'field': [15086717584, 0, -971429216, 0, 80770960, 0, 7193632, 0, -207800, 0, 44152, 0, -848, 0, 40, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [12]}
  • id: 9659028
    {'degree': 16, 'field': [75581027881, 16929999896, -14980082104, -3813579288, 1692301364, 254069080, -78885368, -5547600, 2147845, -578760, 188836, -41944, 8750, -840, 140, -8, 1], 'lmfdb_label': '221880.e1', 'torsion': [2, 8]}
  • id: 9659031
    {'degree': 16, 'field': [646908141636, 0, 16530999912, 0, -505214100, 0, 12902712, 0, 2352144, 0, 95748, 0, 3340, 0, 88, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [12]}
  • id: 9659026
    {'degree': 16, 'field': [2739260015041, 0, 77281051692, 0, -8230357322, 0, -99783936, 0, 9982215, 0, 15624, 0, -5102, 0, 12, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [4, 4]}
  • id: 9659027
    {'degree': 16, 'field': [31904897887521, 12538215544176, 2010756167226, -358337925864, 17134457814, 9931730976, 869058924, -105857448, 37972219, -1225888, 804804, -56680, 6422, -752, 70, 0, 1], 'lmfdb_label': '221880.e1', 'torsion': [2, 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: 5504352
    {'conductor': 221880, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '221880.e1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5504353
    {'conductor': 221880, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '221880.e1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5504354
    {'conductor': 221880, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221880.e1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5504355
    {'conductor': 221880, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '221880.e1', 'prime': 43, '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: 3081133
    {'adelic_gens': [[1939, 1936, 4538, 1941], [1, 0, 8, 1], [1, 8, 0, 1], [3448, 3, 3445, 2], [1, 4, 4, 17], [5153, 8, 5152, 9], [1936, 4523, 649, 678], [7, 6, 5154, 5155], [2068, 1, 4151, 6], [2396, 5159, 3457, 5154]], 'adelic_image': '5160.48.0.?', 'conductor': 221880, 'lmfdb_label': '221880.e1', 'prime': 0}
  • id: 813733
    {'conductor': 221880, 'elladic_image': '4.6.0.1', 'lmfdb_label': '221880.e1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 221880.e does not appear in ec_padic