Elliptic curve data - 57222.t4

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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': '57222i1', 'Cnumber': 1, 'abc_quality': 0.9867709317256699, 'absD': 87445554563737429475328, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 408, 'ainvs': [1, -1, 0, -15208101, 17855409685], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 57222, 'degree': 6193152, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1150333500080677126271145228', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 4], 'jinv': [22106889268753393, 4969545596928], 'lmfdb_iso': '57222.t', 'lmfdb_label': '57222.t4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -5847, -135063], '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.1.2', '24.24.0-8.m.1.1', '34.6.0.a.1', '68.12.0.g.1', '136.24.0.?', '204.24.0.?', '408.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, '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': '1.1491205336459048268047245954', 'prec': 100}, 'szpiro_ratio': 5.588985055575591, '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': '0.0019693205385472607089309460448', 'prec': 110}, 'conductor': 57222, 'gens': [], 'heights': [], 'lmfdb_label': '57222.t4', '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': [[-4390, 2195, 1]], 'xcoord_integral_points': [-4390]}
• 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.t4'}
• ec_torsion_growth •

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

  
  
  • id: 2755763
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '57222.t4', 'torsion': [2, 2]}
  • id: 2755765
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '57222.t4', 'torsion': [4]}
  • id: 2755764
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '57222.t4', 'torsion': [4]}
  • id: 2755766
    {'degree': 4, 'field': [16, 4, 5, -1, 1], 'lmfdb_label': '57222.t4', 'torsion': [2, 4]}
  • id: 2755770
    {'degree': 8, 'field': [-19296, -37278, -10143, 15438, -1401, 30, -17, -2, 1], 'lmfdb_label': '57222.t4', 'torsion': [6]}
  • id: 2755768
    {'degree': 8, 'field': [121, 0, 138, 0, 55, 0, 6, 0, 1], 'lmfdb_label': '57222.t4', 'torsion': [8]}
  • id: 2755767
    {'degree': 8, 'field': [4504, -11372, -2563, 774, -532, 132, -16, -2, 1], 'lmfdb_label': '57222.t4', 'torsion': [2, 4]}
  • id: 2755769
    {'degree': 8, 'field': [48400, 106480, 258236, -51876, 12629, -750, 113, -2, 1], 'lmfdb_label': '57222.t4', 'torsion': [8]}
  • id: 2755772
    {'degree': 16, 'field': [172, -848, 1378, -452, -679, -68, 900, -188, -238, -112, 162, -40, 20, -4, 4, -4, 1], 'lmfdb_label': '57222.t4', 'torsion': [2, 8]}
  • id: 2755774
    {'degree': 16, 'field': [2534464, 0, -2022825, 0, 810946, 0, -1102519, 0, 198975, 0, -10399, 0, -41, 0, 6, 0, 1], 'lmfdb_label': '57222.t4', 'torsion': [2, 6]}
  • id: 2755773
    {'degree': 16, 'field': [32444416, 226381824, 1645157888, -359561728, 459754176, -102572736, 89970384, -19091920, 7818732, -955368, 323230, -30708, 9083, -406, 109, -2, 1], 'lmfdb_label': '57222.t4', 'torsion': [2, 8]}
  • id: 2755771
    {'degree': 16, 'field': [607573201, -379249514, 118364498, -65207124, 27474829, -7569148, 2871318, -874358, 126300, -49718, 17574, -1156, 469, -180, 2, -2, 1], 'lmfdb_label': '57222.t4', 'torsion': [4, 4]}
  • id: 2755775
    {'degree': 16, 'field': [933424704, 0, 2544508323, 0, 348973210, 0, 42157677, 0, 2619339, 0, 129913, 0, 4119, 0, 102, 0, 1], 'lmfdb_label': '57222.t4', 'torsion': [12]}
  • id: 2755776
    {'degree': 16, 'field': [3078918144, 0, 709358592, 0, 118152448, 0, 10431744, 0, 721344, 0, 25568, 0, 816, 0, 0, 0, 1], 'lmfdb_label': '57222.t4', '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: 1375883
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 28, 'j_denominator_valuation': 28, 'kodaira_symbol': 32, 'lmfdb_label': '57222.t4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1375884
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '57222.t4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1375885
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '57222.t4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1375886
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '57222.t4', '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: 2043990
    {'adelic_gens': [[271, 0, 0, 407], [331, 54, 90, 19], [1, 0, 8, 1], [260, 135, 33, 266], [361, 360, 30, 367], [1, 8, 0, 1], [1, 4, 4, 17], [401, 8, 400, 9], [7, 6, 402, 403]], 'adelic_image': '408.48.0.?', 'conductor': 57222, 'lmfdb_label': '57222.t4', 'prime': 0}
  • id: 242846
    {'conductor': 57222, 'elladic_image': '8.12.0.11', 'lmfdb_label': '57222.t4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 57222.t does not appear in ec_padic