Elliptic curve data - 27200.i1

Formats: - HTML - YAML - JSON - 2024-05-01T16:11:57.479495

• 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': '27200ce', 'Clabel': '27200ce1', 'Cnumber': 1, 'abc_quality': 0.8484639388765889, 'absD': 1740800000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 680, 'ainvs': [0, 1, 0, -13633, 604863], 'analytic_rank': 0, 'bad_primes': [2, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 27200, 'degree': 49152, 'elladic_images': ['4.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1867522164689448943636575539', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2], 'jinv': [68417929, 425], 'lmfdb_iso': '27200.i', 'lmfdb_label': '27200.i1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -8, -13], 'min_quad_twist_disc': -40, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.b.1', '34.6.0.a.1', '40.12.0-4.b.1.3', '68.12.0.e.1', '136.24.0.?', '340.24.0.?', '680.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.65768751058802325706257029490', 'prec': 107}, 'szpiro_ratio': 3.9344365257505642, '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, -2, 0, 0, 0, -2, 0, 1, 0, 2, 0, 2, 0, 0, 0, -1, 0, 0, 0], 'aplist': [0, -2, 0, -2, 2, 2, -1, 0, 6, 6, 10, 2, 10, -4, 12, -10, 8, 14, -8, 2, 14, 14, -4, 6, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 27200, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '27200.i', 'trace_hash': 188742259596854163}
• 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': '0.093153702692626599793961392555', 'prec': 107}, 'conductor': 27200, 'gens': [], 'heights': [], 'lmfdb_label': '27200.i1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.84304074712837674972115874449', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6860814942567534994423174889843086955', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[63, 0, 1]], 'xcoord_integral_points': [63]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '5': 'a', '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '27200.i1'}
• ec_torsion_growth •

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

  
  
  • id: 1362657
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '27200.i1', 'torsion': [2, 2]}
  • id: 1362658
    {'degree': 4, 'field': [425, 0, -40, 0, 1], 'lmfdb_label': '27200.i1', 'torsion': [4]}
  • id: 1362661
    {'degree': 8, 'field': [-10800, 0, 2120, 0, -360, 0, 0, 0, 1], 'lmfdb_label': '27200.i1', 'torsion': [6]}
  • id: 1362659
    {'degree': 8, 'field': [1024, 0, 1440, 0, 124, 0, -40, 0, 1], 'lmfdb_label': '27200.i1', 'torsion': [2, 4]}
  • id: 1362660
    {'degree': 8, 'field': [10000, 0, 0, 0, 225, 0, 0, 0, 1], 'lmfdb_label': '27200.i1', 'torsion': [2, 4]}
  • id: 1362662
    {'degree': 16, 'field': [4096, 0, 0, 0, 28432, 0, 0, 0, 8289, 0, 0, 0, 338, 0, 0, 0, 1], 'lmfdb_label': '27200.i1', 'torsion': [4, 4]}
  • id: 1362663
    {'degree': 16, 'field': [6161, -18184, 18752, -10972, 8948, -7120, 5070, -4020, 1477, -608, 746, -308, 68, -32, 30, -8, 1], 'lmfdb_label': '27200.i1', 'torsion': [8]}
  • id: 1362664
    {'degree': 16, 'field': [81497936, -72323648, 70888456, 11285568, -26102504, 22939136, -4978736, -2245856, 508497, 38824, -11716, 2696, -874, 168, -4, -8, 1], 'lmfdb_label': '27200.i1', '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: 627547
    {'conductor': 27200, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '27200.i1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 627548
    {'conductor': 27200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '27200.i1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 627549
    {'conductor': 27200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27200.i1', 'prime': 17, '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: 1845464
    {'adelic_gens': [[169, 672, 336, 647], [86, 1, 103, 4], [1, 0, 8, 1], [3, 8, 28, 75], [5, 8, 48, 77], [673, 8, 672, 9], [339, 672, 0, 679], [401, 674, 142, 5], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '680.48.0.?', 'conductor': 27200, 'lmfdb_label': '27200.i1', 'prime': 0}
  • id: 123117
    {'conductor': 27200, 'elladic_image': '4.6.0.3', 'lmfdb_label': '27200.i1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 27200.i does not appear in ec_padic