Elliptic curve data - 162240.gr1

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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': '162240es', 'Clabel': '162240es1', 'Cnumber': 1, 'abc_quality': 1.055487769231265, 'absD': 168130926288000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, 1, 0, -232925, 38431875], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 162240, 'degree': 1806336, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0360300975834886375518877829', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 173, 'isogeny_degrees': [1, 2], 'jinv': [621217777580032, 74733890625], 'lmfdb_iso': '162240.gr', 'lmfdb_label': '162240.gr1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -58231, 4833100], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.f.1', '26.6.0.b.1', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 25, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.57564236817472967239557306109', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 13], [3, 4, 10816], [5, 6, 32448], [7, 2, 54080], [13, 50, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.81717010775148336235748915463', 'prec': 103}, 'szpiro_ratio': 4.058490000143377, '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, 0, 1, 0, 1, 0, -2, 0, 1, 0, -4, 0, 0, 0, 1, 0, -2, 0, -6, 0], 'aplist': [0, 1, 1, -2, -4, 0, -2, -6, 0, -10, 2, -8, 2, -4, -8, -2, 0, -10, 2, 12, -8, 8, -16, 6, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 162240, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '162240.gr', 'trace_hash': 2283446808198866299}
• 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': '0.017042241971010716710720631138', 'prec': 107}, 'conductor': 162240, 'gens': [[550, 8775, 1], [355, 780, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.37006864005348194395535360821', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.5898634657106897162644921260', 'prec': 100}], 'lmfdb_label': '162240.gr1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.31123335490137851257965246714', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '15.049364859513233389237601747160682895', 'prec': 130}, 'tamagawa_product': 336, 'torsion_generators': [[199, 0, 1]], 'xcoord_integral_points': [-530, -425, -125, 150, 163, 190, 199, 355, 550, 775, 1495, 3358, 12835]}
• lmfdb_label 162240.gr1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7248676
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '162240.gr1', 'torsion': [2, 2]}
  • id: 7248677
    {'degree': 4, 'field': [208, 0, -26, 0, 1], 'lmfdb_label': '162240.gr1', 'torsion': [4]}
  • id: 7248680
    {'degree': 8, 'field': [-8112, 0, 5408, 0, -312, 0, 0, 0, 1], 'lmfdb_label': '162240.gr1', 'torsion': [6]}
  • id: 7248678
    {'degree': 8, 'field': [1521, 0, 2704, 0, -793, 0, 26, 0, 1], 'lmfdb_label': '162240.gr1', 'torsion': [2, 4]}
  • id: 7248679
    {'degree': 8, 'field': [43264, 0, 5408, 0, 468, 0, 26, 0, 1], 'lmfdb_label': '162240.gr1', 'torsion': [2, 4]}
  • id: 7248682
    {'degree': 16, 'field': [20820969, 0, -20049822, 0, 4231422, 0, 711828, 0, -210405, 0, -12844, 0, 1326, 0, 0, 0, 1], 'lmfdb_label': '162240.gr1', 'torsion': [2, 6]}
  • id: 7248681
    {'degree': 16, 'field': [86767032, 108982800, 93375096, 55914768, 28349044, 12692688, 5081052, 1683944, 376734, 33552, -10188, -5196, -402, -124, 24, 0, 1], 'lmfdb_label': '162240.gr1', 'torsion': [8]}
• 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: 4014216
    {'conductor': 162240, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '162240.gr1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4014217
    {'conductor': 162240, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '162240.gr1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 14}
  • id: 4014218
    {'conductor': 162240, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '162240.gr1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 4014219
    {'conductor': 162240, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '162240.gr1', 'prime': 13, '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: 2713000
    {'adelic_gens': [[1, 2, 2, 5], [53, 4, 106, 9], [112, 1, 11, 0], [3, 4, 8, 11], [153, 4, 152, 5], [1, 4, 0, 1], [41, 118, 116, 39], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 162240, 'lmfdb_label': '162240.gr1', 'prime': 0}
  • id: 617029
    {'conductor': 162240, 'elladic_image': '2.3.0.1', 'lmfdb_label': '162240.gr1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 162240.gr does not appear in ec_padic