Elliptic curve data - 57222.t1

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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': '57222i4', 'Cnumber': 4, 'abc_quality': 1.0382088586045655, 'absD': 30397324217302601856, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 408, 'ainvs': [1, -1, 0, -3652446501, 84962752990357], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 57222, 'degree': 24772608, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8081805305680130220443466442', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 4], 'jinv': [306234591284035366263793, 1727485056], 'lmfdb_iso': '57222.t', 'lmfdb_label': '57222.t1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1404247, -640608535], 'min_quad_twist_disc': -51, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '12.12.0-4.c.1.1', '24.24.0-8.m.1.3', '136.24.0.?', '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': 7.090074281337202, '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.t1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10140580604047455773075164943', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.40562322416189823092300659773488472946', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[139571, -139571, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 0], '3': 'a', '11': [0, 0], '17': 'a'}, 'iwp0': 3, 'lmfdb_label': '57222.t1'}
• ec_torsion_growth •

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

  
  
  • id: 2755801
    {'degree': 2, 'field': [-102, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [4]}
  • id: 2755799
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [2, 2]}
  • id: 2755800
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [4]}
  • id: 2755802
    {'degree': 4, 'field': [289, 0, -68, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [2, 4]}
  • id: 2755806
    {'degree': 8, 'field': [-19296, -37278, -10143, 15438, -1401, 30, -17, -2, 1], 'lmfdb_label': '57222.t1', 'torsion': [6]}
  • id: 2755805
    {'degree': 8, 'field': [484, 0, 80, 0, 54, 0, -16, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [8]}
  • id: 2755804
    {'degree': 8, 'field': [12224446, 1558858, -1057309, -60750, 28541, 678, -295, -2, 1], 'lmfdb_label': '57222.t1', 'torsion': [8]}
  • id: 2755803
    {'degree': 8, 'field': [16924996, 0, 0, 0, 4114, 0, 0, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [2, 4]}
  • id: 2755809
    {'degree': 16, 'field': [-1260252450, 553345380, 3106210578, -1931223684, -916143269, 776885788, 7242922, -87852108, 8575149, 4263884, -620418, -98252, 17457, 1044, -218, -4, 1], 'lmfdb_label': '57222.t1', 'torsion': [2, 8]}
  • id: 2755808
    {'degree': 16, 'field': [1089, 0, 6636, 0, 109840, 0, -25200, 0, 10719, 0, -2048, 0, 144, 0, -12, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [2, 8]}
  • id: 2755811
    {'degree': 16, 'field': [12027024, 0, 22167456, 0, 12458212, 0, 1303968, 0, -631176, 0, -83096, 0, -2856, 0, 0, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [12]}
  • id: 2755810
    {'degree': 16, 'field': [648822784, 0, -258921600, 0, 51900544, 0, -35280608, 0, 3183600, 0, -83192, 0, -164, 0, 12, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [2, 6]}
  • id: 2755812
    {'degree': 16, 'field': [238956724224, 0, -325697065344, 0, 22334285440, 0, -1349045664, 0, 41909424, 0, -1039304, 0, 16476, 0, -204, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [12]}
  • id: 2755807
    {'degree': 16, 'field': [286594799250321, 0, -835011471012, 0, -276250072682, 0, 338170784, 0, 102002535, 0, -16472, 0, -16446, 0, -4, 0, 1], 'lmfdb_label': '57222.t1', 'torsion': [4, 4]}
• 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: 1375895
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '57222.t1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1375896
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '57222.t1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1375897
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '57222.t1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1375898
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '57222.t1', 'prime': 17, 'reduction_type': 0, '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: 2043987
    {'adelic_gens': [[1, 8, 0, 1], [401, 8, 400, 9], [260, 135, 33, 266], [1, 0, 8, 1], [271, 0, 0, 407], [259, 120, 210, 397], [1, 4, 4, 17], [7, 6, 402, 403], [256, 195, 225, 118]], 'adelic_image': '408.48.0.?', 'conductor': 57222, 'lmfdb_label': '57222.t1', 'prime': 0}
  • id: 242843
    {'conductor': 57222, 'elladic_image': '8.12.0.11', 'lmfdb_label': '57222.t1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 57222.t does not appear in ec_padic