Elliptic curve data - 228672.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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '228672h', 'Clabel': '228672h1', 'Cnumber': 1, 'abc_quality': 0.9163188303079978, 'absD': 6292785560813568, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 1588, 'ainvs': [0, 0, 0, -275916, 55914896], 'analytic_rank': 1, 'bad_primes': [2, 3, 397], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 228672, 'degree': 1720320, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9054450758943060597299725895', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 19, 'isogeny_degrees': [1], 'jinv': [-12155894380657, 32928768], 'lmfdb_iso': '228672.t', 'lmfdb_label': '228672.t1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -479, 3845], 'min_quad_twist_disc': 24, 'modell_images': [], 'modm_images': ['1588.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3938524560350518350495221097', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3573], [3, 8, 25408], [397, 398, 576]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.31641816072033324990650178885', 'prec': 103}, 'szpiro_ratio': 3.987167997802679, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, -2, 0, -1, 0, 0, 0, 2, 0, 2, 0, 0, 0, -6, 0, -6, 0], 'aplist': [0, 0, -2, -1, 2, 2, -6, -6, 6, -9, 2, -9, 10, 2, -10, 8, 3, 6, -10, 5, -9, 12, 6, -12, 7], 'class_deg': 1, 'class_size': 1, 'conductor': 228672, 'isogeny_matrix': [[1]], 'lmfdb_iso': '228672.t', 'trace_hash': 423775057312775691}
• 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': '0.022128472488099728555818108761', 'prec': 107}, 'conductor': 228672, 'gens': [[-110, 9216, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3938524560350518350495221097', 'prec': 100}], 'lmfdb_label': '228672.t1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.42498789496262422351565151691', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7389633694305632619572588309927145247', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [-110, 389]}
• lmfdb_label 228672.t1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9921883
    {'degree': 3, 'field': [-16, -11, 0, 1], 'lmfdb_label': '228672.t1', 'torsion': [2]}
  • id: 9921884
    {'degree': 6, 'field': [1784, -1560, 426, -26, -1, -2, 1], 'lmfdb_label': '228672.t1', 'torsion': [2, 2]}
  • id: 9921885
    {'degree': 8, 'field': [-25392, 0, -3126, 0, -252, 0, -20, 0, 1], 'lmfdb_label': '228672.t1', 'torsion': [3]}
  • id: 9921886
    {'degree': 12, 'field': [-47699898, 32491464, -10637564, -861780, 335778, -170344, 78622, -9368, 1501, -488, 20, -4, 1], 'lmfdb_label': '228672.t1', 'torsion': [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: 5670193
    {'conductor': 228672, 'conductor_valuation': 6, 'discriminant_valuation': 28, 'j_denominator_valuation': 10, 'kodaira_symbol': -22, 'lmfdb_label': '228672.t1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5670194
    {'conductor': 228672, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '228672.t1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5670195
    {'conductor': 228672, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '228672.t1', 'prime': 397, '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

  
  {'adelic_gens': [[1, 0, 2, 1], [1, 2, 0, 1], [1, 1, 1587, 0], [1587, 2, 1586, 3], [795, 2, 795, 3], [5, 2, 5, 3]], 'adelic_image': '1588.2.0.?', 'conductor': 228672, 'lmfdb_label': '228672.t1', 'prime': 0}
• lmfdb_iso 228672.t does not appear in ec_padic