Elliptic curve data - 227136.gz1

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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': '227136bg', 'Clabel': '227136bg2', 'Cnumber': 2, 'abc_quality': 0.9965723308648884, 'absD': 15408441065472, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 168, 'ainvs': [0, 1, 0, -330113, 72893055], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 227136, 'degree': 1161216, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7438162590066098054446893568', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 181, 'isogeny_degrees': [1, 3], 'jinv': [531373116625, 2058], 'lmfdb_iso': '227136.gz', 'lmfdb_label': '227136.gz1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -5158, -143014], 'min_quad_twist_disc': -8, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '24.8.0-3.a.1.3', '84.8.0.?', '168.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.7022833478576281751084536620', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 3549], [3, 4, 10816], [7, 8, 32448], [13, 62, 1344]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15088763098715373736565463924', 'prec': 107}, 'szpiro_ratio': 4.032591429473018, '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, 1, 0, 0, 0, -1, 0, 1, 0, 3, 0, 0, 0, 0, 0, 3, 0, 5, 0], 'aplist': [0, 1, 0, -1, 3, 0, 3, 5, -6, 3, 4, 4, -3, 8, -9, 9, -6, -5, 14, 6, -4, 1, -6, -9, 8], 'class_deg': 3, 'class_size': 2, 'conductor': 227136, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '227136.gz', 'trace_hash': 1546119632269700365}
• 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': '0.030573167982411307131296902160', 'prec': 107}, 'conductor': 227136, 'gens': [[119337, 139296, 19]], 'heights': [{'__RealLiteral__': 0, 'data': '8.7022833478576281751084536620', 'prec': 100}], 'lmfdb_label': '227136.gz1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.61399741784451380929648751791', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.686359009871789285879300386183135672', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 227136.gz1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9860676
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '227136.gz1', 'torsion': [3]}
  • id: 9860677
    {'degree': 3, 'field': [103, -43, -1, 1], 'lmfdb_label': '227136.gz1', 'torsion': [2]}
  • id: 9860680
    {'degree': 6, 'field': [538, 928, 356, -104, -61, -2, 1], 'lmfdb_label': '227136.gz1', 'torsion': [6]}
  • id: 9860678
    {'degree': 6, 'field': [2800, -3920, 1166, 172, -73, -2, 1], 'lmfdb_label': '227136.gz1', 'torsion': [2, 2]}
  • id: 9860679
    {'degree': 6, 'field': [6092, 936, 12, -156, 6, 0, 1], 'lmfdb_label': '227136.gz1', 'torsion': [3]}
  • id: 9860681
    {'degree': 12, 'field': [-152568, -293592, -181844, 27260, 72572, 16120, -8032, -2144, 422, 70, -37, -1, 1], 'lmfdb_label': '227136.gz1', 'torsion': [4]}
  • id: 9860683
    {'degree': 12, 'field': [-2400, 25920, 149488, -644752, 313572, 167152, -68152, -13680, 4592, 424, -120, -4, 1], 'lmfdb_label': '227136.gz1', 'torsion': [2, 6]}
  • id: 9860682
    {'degree': 12, 'field': [37112464, -5702112, 802992, -1911936, 109608, 13104, 36448, 0, 24, -312, -6, 0, 1], 'lmfdb_label': '227136.gz1', 'torsion': [3, 3]}
  • id: 9860684
    {'degree': 18, 'field': [-8742609504, 0, 257464729872, 0, -87426032400, 0, 11892577140, 0, -821186856, 0, 28869624, 0, -522666, 0, 13860, 0, -84, 0, 1], 'lmfdb_label': '227136.gz1', 'torsion': [9]}
  • id: 9860685
    {'degree': 18, 'field': [272097792, 0, 0, 0, 0, 0, 58414212, 0, 0, 0, 0, 0, 21444, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '227136.gz1', 'torsion': [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: 5631894
    {'conductor': 227136, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '227136.gz1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5631895
    {'conductor': 227136, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '227136.gz1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5631896
    {'conductor': 227136, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '227136.gz1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5631897
    {'conductor': 227136, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '227136.gz1', 'prime': 13, 'reduction_type': 0, '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: 3112756
    {'adelic_gens': [[83, 162, 81, 149], [73, 6, 51, 19], [1, 0, 6, 1], [41, 162, 0, 167], [4, 3, 9, 7], [163, 6, 162, 7], [3, 4, 8, 11], [122, 51, 1, 106], [1, 6, 0, 1]], 'adelic_image': '168.16.0.?', 'conductor': 227136, 'lmfdb_label': '227136.gz1', 'prime': 0}
  • id: 829849
    {'conductor': 227136, 'elladic_image': '3.4.0.1', 'lmfdb_label': '227136.gz1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 227136.gz does not appear in ec_padic