Elliptic curve data - 57222.t3

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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': '57222i', 'Clabel': '57222i3', 'Cnumber': 3, 'abc_quality': 1.0176943714578126, 'absD': 362919833076833561534746752, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 408, 'ainvs': [1, -1, 0, -213300261, 1509291282325], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 57222, 'degree': 24772608, 'elladic_images': ['8.12.0.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8081805305680130220443466442', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 4], 'jinv': [-60992553706117024753, 20624795251201152], 'lmfdb_iso': '57222.t', 'lmfdb_label': '57222.t3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -82007, -11384343], 'min_quad_twist_disc': -51, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.d.1', '24.24.0-8.d.1.3', '136.24.0.?', '204.12.0.?', '408.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2601], [3, 8, 6358], [7, 2, 28611], [11, 12, 5202], [17, 162, 198]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8422677142058501362219567168', 'prec': 100}, 'szpiro_ratio': 6.35420754563965, '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, 2, 0, -4, -1, 0, -2, -1, 0, -2, 4, 0, 1, 0, 0, -4, 2], 'aplist': [-1, 0, 2, -4, -1, -2, 0, -4, -4, 2, 4, 6, -6, -4, 0, -6, -4, 6, -4, 4, -10, -4, -12, 6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 57222, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '57222.t', 'trace_hash': 818154118872725185}
• 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': '0.00049233013463681517723273651120', 'prec': 113}, 'conductor': 57222, 'gens': [], 'heights': [], 'lmfdb_label': '57222.t3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.050702903020237278865375824717', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.40562322416189823092300659773488472946', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-69325, 69325, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 1], '3': 'a', '11': [0, 0], '17': 'a'}, 'iwp0': 3, 'lmfdb_label': '57222.t3'}
• ec_torsion_growth •

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

  
  
  • id: 2755786
    {'degree': 2, 'field': [-51, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [4]}
  • id: 2755785
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [2, 2]}
  • id: 2755787
    {'degree': 2, 'field': [102, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [4]}
  • id: 2755788
    {'degree': 4, 'field': [625, 0, 52, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [2, 4]}
  • id: 2755792
    {'degree': 8, 'field': [-19296, -37278, -10143, 15438, -1401, 30, -17, -2, 1], 'lmfdb_label': '57222.t3', 'torsion': [6]}
  • id: 2755790
    {'degree': 8, 'field': [4, 0, -24, 0, -19, 0, 12, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [8]}
  • id: 2755791
    {'degree': 8, 'field': [324, 0, -144, 0, 82, 0, 8, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [8]}
  • id: 2755789
    {'degree': 8, 'field': [2500, 0, 0, 0, -2, 0, 0, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [2, 4]}
  • id: 2755794
    {'degree': 16, 'field': [676, 0, 13288, 0, 13064, 0, 708, 0, -1267, 0, 192, 0, 26, 0, 4, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [2, 8]}
  • id: 2755795
    {'degree': 16, 'field': [6561, 0, -2268, 0, -8936, 0, -1416, 0, 13983, 0, -1384, 0, 24, 0, -12, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [2, 8]}
  • id: 2755793
    {'degree': 16, 'field': [390625, 0, -437500, 0, 245000, 0, -121800, 0, 38351, 0, -4872, 0, 392, 0, -28, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [4, 4]}
  • id: 2755796
    {'degree': 16, 'field': [631416384, 0, 208228968, 0, -93007116, 0, 30338208, 0, -2974716, 0, 128196, 0, 1372, 0, -104, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [2, 6]}
  • id: 2755797
    {'degree': 16, 'field': [933424704, 0, -2544508323, 0, 348973210, 0, -42157677, 0, 2619339, 0, -129913, 0, 4119, 0, -102, 0, 1], 'lmfdb_label': '57222.t3', 'torsion': [12]}
  • id: 2755798
    {'degree': 16, 'field': [238956724224, 0, 325697065344, 0, 22334285440, 0, 1349045664, 0, 41909424, 0, 1039304, 0, 16476, 0, 204, 0, 1], 'lmfdb_label': '57222.t3', '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: 1375891
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '57222.t3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1375892
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '57222.t3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1375893
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '57222.t3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1375894
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '57222.t3', 'prime': 17, '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: 2043989
    {'adelic_gens': [[271, 0, 0, 407], [88, 297, 315, 166], [167, 264, 396, 239], [1, 0, 8, 1], [256, 195, 123, 16], [7, 6, 402, 403], [401, 8, 400, 9], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '408.48.0.?', 'conductor': 57222, 'lmfdb_label': '57222.t3', 'prime': 0}
  • id: 242845
    {'conductor': 57222, 'elladic_image': '8.12.0.16', 'lmfdb_label': '57222.t3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 57222.t does not appear in ec_padic