Elliptic curve data - 162240.ba1

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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': '162240dw', 'Clabel': '162240dw1', 'Cnumber': 1, 'abc_quality': 1.030848407805706, 'absD': 66406035920336782884864000, 'adelic_genus': 5, 'adelic_index': 144, 'adelic_level': 1560, 'ainvs': [0, -1, 0, -242938401, 1403801086401], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 162240, 'degree': 64696320, 'elladic_images': ['2.3.0.1', '3.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7196373301839811828632548198', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2], 'jinv': [570403428460237, 23887872000], 'lmfdb_iso': '162240.ba', 'lmfdb_label': '162240.ba1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -22461, -1257261], 'min_quad_twist_disc': -104, 'modell_images': ['2B', '3Ns'], 'modm_images': ['2.3.0.a.1', '3.6.0.b.1', '6.18.0.b.1', '24.36.0.c.1', '30.36.0.d.1', '39.12.0.a.1', '40.6.0.e.1', '78.36.0.?', '104.6.0.?', '120.72.1.?', '130.6.0.?', '312.72.1.?', '390.72.1.?', '520.12.0.?', '1560.144.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '28.020233525647239511516308260', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 65], [3, 4, 10816], [5, 6, 32448], [13, 62, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.75620454124791066669729105644', 'prec': 103}, 'szpiro_ratio': 5.796410124475612, '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, 0, 0, 1, 0, 6, 0, 0, 0, 1, 0, 6, 0, -6, 0], 'aplist': [0, -1, -1, 0, 6, 0, 6, -6, 6, 6, 0, 6, -12, -8, 0, 12, 6, -10, 0, -12, -6, 8, 0, 0, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 162240, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '162240.ba', 'trace_hash': 365037559316718366}
• 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': '0.00058771133330297362081933838226', 'prec': 113}, 'conductor': 162240, 'gens': [[703626886056975, 17235135583326211069584, 137269]], 'heights': [{'__RealLiteral__': 0, 'data': '28.020233525647239511516308260', 'prec': 100}], 'lmfdb_label': '162240.ba1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.061316469206761930687983554185', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.8724071445665089941378097963171542657', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[7549, 0, 1]], 'xcoord_integral_points': [7549]}
• lmfdb_label 162240.ba1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7248466
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '162240.ba1', 'torsion': [2, 2]}
  • id: 7248469
    {'degree': 4, 'field': [-156, 0, -26, 0, 1], 'lmfdb_label': '162240.ba1', 'torsion': [6]}
  • id: 7248467
    {'degree': 4, 'field': [204, -20, 21, -2, 1], 'lmfdb_label': '162240.ba1', 'torsion': [4]}
  • id: 7248468
    {'degree': 4, 'field': [208, 0, 26, 0, 1], 'lmfdb_label': '162240.ba1', 'torsion': [6]}
  • id: 7248470
    {'degree': 8, 'field': [-169064, -210600, -84442, -9360, 969, 0, -58, 0, 1], 'lmfdb_label': '162240.ba1', 'torsion': [2, 4]}
  • id: 7248471
    {'degree': 8, 'field': [4096, 0, 1192, 0, 188, 0, 22, 0, 1], 'lmfdb_label': '162240.ba1', 'torsion': [2, 4]}
  • id: 7248473
    {'degree': 8, 'field': [17104, -6704, 8126, -2912, 1627, -208, 74, -4, 1], 'lmfdb_label': '162240.ba1', 'torsion': [2, 6]}
  • id: 7248474
    {'degree': 8, 'field': [36011, -4364, 4760, -736, 229, 164, -50, -4, 1], 'lmfdb_label': '162240.ba1', 'torsion': [2, 6]}
  • id: 7248472
    {'degree': 8, 'field': [43264, 0, -5408, 0, 468, 0, -26, 0, 1], 'lmfdb_label': '162240.ba1', 'torsion': [3, 6]}
  • id: 7248478
    {'degree': 16, 'field': [3264, -7872, 2512, 12752, -15452, 680, 9734, -5656, -181, 906, 293, -566, 236, -38, 1, -2, 1], 'lmfdb_label': '162240.ba1', 'torsion': [12]}
  • id: 7248477
    {'degree': 16, 'field': [4096, 0, 13312, 0, 18752, 0, 13728, 0, 2516, 0, -1716, 0, 293, 0, -26, 0, 1], 'lmfdb_label': '162240.ba1', 'torsion': [12]}
  • id: 7248475
    {'degree': 16, 'field': [490844025, 0, 118079648, 0, 47225952, 0, 5132472, 0, 51350, 0, 5920, 0, 1584, 0, -24, 0, 1], 'lmfdb_label': '162240.ba1', 'torsion': [8]}
  • id: 7248476
    {'degree': 16, 'field': [1316104219, -461567388, 807173420, -236411840, 211305083, -49270956, 31311950, -5652180, 2881762, -390324, 167200, -16360, 5943, -388, 118, -4, 1], 'lmfdb_label': '162240.ba1', 'torsion': [6, 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: 4014092
    {'conductor': 162240, 'conductor_valuation': 6, 'discriminant_valuation': 36, 'j_denominator_valuation': 18, 'kodaira_symbol': -30, 'lmfdb_label': '162240.ba1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4014093
    {'conductor': 162240, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '162240.ba1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4014094
    {'conductor': 162240, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '162240.ba1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4014095
    {'conductor': 162240, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '162240.ba1', '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: 2712680
    {'adelic_gens': [[10, 3, 1221, 1552], [7, 12, 144, 247], [492, 5, 187, 1488], [781, 12, 6, 73], [1, 0, 12, 1], [1, 6, 6, 37], [5, 12, 1512, 1445], [1, 12, 0, 1], [329, 978, 1386, 731], [1549, 12, 1548, 13], [783, 1042, 22, 795]], 'adelic_image': '1560.144.5.?', 'conductor': 162240, 'lmfdb_label': '162240.ba1', 'prime': 0}
  • id: 616748
    {'conductor': 162240, 'elladic_image': '2.3.0.1', 'lmfdb_label': '162240.ba1', 'modell_image': '2B', 'prime': 2}
  • id: 616749
    {'conductor': 162240, 'elladic_image': '3.6.0.1', 'lmfdb_label': '162240.ba1', 'modell_image': '3Ns', 'prime': 3}
• lmfdb_iso 162240.ba does not appear in ec_padic