Elliptic curve data - 21879.a2

Formats: - HTML - YAML - JSON - 2025-10-28T08:30:37.902611

• 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': '21879i', 'Clabel': '21879i2', 'Cnumber': 2, 'abc_quality': 0.8608596561528015, 'absD': 40099546773, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [1, -1, 1, 238, 9470], 'analytic_rank': 1, 'bad_primes': [3, 11, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 21879, 'degree': 21504, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.71467353553569420947689330620', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [2053225511, 55006237], 'lmfdb_iso': '21879.a', 'lmfdb_label': '21879.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 26, -351], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '52.6.0.a.1', '68.6.0.c.1', '884.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2274740253234367923781052867', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 117], [3, 2, 2431], [11, 12, 1989], [13, 14, 1683], [17, 18, 1287]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.16536739120163936377927068774', 'prec': 103}, 'szpiro_ratio': 3.1868920522200406, '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, -4, 0, 0, 3, 0, 4, -1, 0, 1, 0, 0, -1, -1, 0, 4, 4], 'aplist': [-1, 0, -4, 0, -1, 1, -1, 4, 6, 2, -4, 8, 0, -8, -8, -10, -4, 10, -4, -16, 0, -6, 4, 18, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 21879, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '21879.a', 'trace_hash': 1822342059199939554}
• 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': '0.23946522498369973643774125556', 'prec': 103}, 'conductor': 21879, 'gens': [[13, 114, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2274740253234367923781052867', 'prec': 100}], 'lmfdb_label': '21879.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.86278337855433511158817069414', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1180883733124885781934294544077594080', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-69, 65, 2]], 'xcoord_integral_points': [13, 21]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 1], '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '21879.a2'}
• ec_torsion_growth •

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

  
  
  • id: 1112404
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '21879.a2', 'torsion': [2, 2]}
  • id: 1112405
    {'degree': 4, 'field': [-104, -44, -1, -1, 1], 'lmfdb_label': '21879.a2', 'torsion': [4]}
  • id: 1112408
    {'degree': 8, 'field': [-243, 0, -73, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '21879.a2', 'torsion': [6]}
  • id: 1112407
    {'degree': 8, 'field': [3636, 6084, 1662, -1638, 217, -78, 8, 0, 1], 'lmfdb_label': '21879.a2', 'torsion': [2, 4]}
  • id: 1112406
    {'degree': 8, 'field': [52009, -2828, 12872, 2764, -518, 68, 8, -4, 1], 'lmfdb_label': '21879.a2', 'torsion': [2, 4]}
  • id: 1112409
    {'degree': 16, 'field': [116985856, 0, -180488365824, 0, -34193218384, 0, -2451051616, 0, -84277128, 0, -1294696, 0, -2037, 0, 152, 0, 1], 'lmfdb_label': '21879.a2', 'torsion': [8]}
  • id: 1112410
    {'degree': 16, 'field': [405659881, 0, 580295834, 0, 180439489, 0, 28117992, 0, 2336658, 0, 125694, 0, 4624, 0, 104, 0, 1], 'lmfdb_label': '21879.a2', '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: 499233
    {'conductor': 21879, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21879.a2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 499234
    {'conductor': 21879, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '21879.a2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 499235
    {'conductor': 21879, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21879.a2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 499236
    {'conductor': 21879, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21879.a2', 'prime': 17, 'reduction_type': -1, '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: 1810368
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [664, 225, 221, 664], [881, 4, 880, 5], [105, 4, 210, 9], [342, 1, 271, 0]], 'adelic_image': '884.12.0.?', 'conductor': 21879, 'lmfdb_label': '21879.a2', 'prime': 0}
  • id: 101261
    {'conductor': 21879, 'elladic_image': '2.3.0.1', 'lmfdb_label': '21879.a2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1028926
    {'lmfdb_iso': '21879.a', 'p': 5, 'prec': 20, 'unit': 88630814835457, 'val': -1}
  • id: 1028910
    {'lmfdb_iso': '21879.a', 'p': 19, 'prec': 20, 'unit': 1161357730587923302365918, 'val': 1}
  • id: 1028922
    {'lmfdb_iso': '21879.a', 'p': 23, 'prec': 20, 'unit': 5691625365905554721342380, 'val': 1}
  • id: 1028917
    {'lmfdb_iso': '21879.a', 'p': 29, 'prec': 20, 'unit': 6014864411543843273618791948, 'val': 1}
  • id: 1028915
    {'lmfdb_iso': '21879.a', 'p': 31, 'prec': 20, 'unit': 12429900352485779307515703778, 'val': 1}
  • id: 1028913
    {'lmfdb_iso': '21879.a', 'p': 37, 'prec': 20, 'unit': 517083515053539846888598838871, 'val': 1}
  • id: 1028916
    {'lmfdb_iso': '21879.a', 'p': 43, 'prec': 20, 'unit': 6629303841109330068883673233930, 'val': 1}
  • id: 1028924
    {'lmfdb_iso': '21879.a', 'p': 47, 'prec': 20, 'unit': 23134975839118315163966190291810, 'val': 1}
  • id: 1028921
    {'lmfdb_iso': '21879.a', 'p': 53, 'prec': 20, 'unit': 448237395078664131077290461837861, 'val': 1}
  • id: 1028919
    {'lmfdb_iso': '21879.a', 'p': 59, 'prec': 20, 'unit': 694703306860245605651977030349127, 'val': 1}
  • id: 1028925
    {'lmfdb_iso': '21879.a', 'p': 61, 'prec': 20, 'unit': 5646291236587564310783784935292218, 'val': 1}
  • id: 1028912
    {'lmfdb_iso': '21879.a', 'p': 67, 'prec': 20, 'unit': 25022266175143124230604257243859895, 'val': 1}
  • id: 1028914
    {'lmfdb_iso': '21879.a', 'p': 71, 'prec': 20, 'unit': 85145545242892668933731675951883485, 'val': 1}
  • id: 1028918
    {'lmfdb_iso': '21879.a', 'p': 79, 'prec': 20, 'unit': 844775412877483342575112443593790074, 'val': 1}
  • id: 1028920
    {'lmfdb_iso': '21879.a', 'p': 83, 'prec': 20, 'unit': 84750936757969634375812278286275670, 'val': 1}
  • id: 1028923
    {'lmfdb_iso': '21879.a', 'p': 89, 'prec': 20, 'unit': 1882516932711931207706316904346152054, 'val': 1}
  • id: 1028911
    {'lmfdb_iso': '21879.a', 'p': 97, 'prec': 20, 'unit': 22161846157811881962524003777282814648, 'val': 1}