Elliptic curve data - 268620.b1

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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': '268620b', 'Clabel': '268620b1', 'Cnumber': 1, 'abc_quality': 1.0028616996197188, 'absD': 4300588336770000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3256, 'ainvs': [0, -1, 0, -929441, 345185766], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 268620, 'degree': 3440640, 'elladic_images': ['4.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0724743326896362266202331254', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [3132662187311104, 151723125], 'lmfdb_iso': '268620.b', 'lmfdb_label': '268620.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -7681, -256550], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.b.1', '74.6.0.?', '88.12.0.?', '148.24.0.?', '3256.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8632738125921191751916765027', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 4477], [3, 4, 89540], [5, 6, 53724], [11, 62, 2220], [37, 38, 7260]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.64247763610380251811685062926', 'prec': 103}, 'szpiro_ratio': 4.226893514456037, '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, -4, 0, 1, 0, 0, 0, -2, 0, 1, 0, -2, 0, 2, 0], 'aplist': [0, -1, -1, -4, 0, -2, -2, 2, 6, 6, 10, -1, 2, 2, -4, 10, -10, -2, 4, 12, 2, -6, 0, -6, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 268620, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '268620.b', 'trace_hash': 236803761939309782}
• 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': '0.015844249288972703520009343671', 'prec': 107}, 'conductor': 268620, 'gens': [[598, 1694, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.8632738125921191751916765027', 'prec': 100}], 'lmfdb_label': '268620.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.41217945148536980476814681101', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7207305181065728798906492193916674374', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[554, 0, 1]], 'xcoord_integral_points': [554, 598]}
• lmfdb_label 268620.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11482472
    {'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '268620.b1', 'torsion': [2, 2]}
  • id: 11482473
    {'degree': 4, 'field': [1125, 54, -64, -2, 1], 'lmfdb_label': '268620.b1', 'torsion': [4]}
  • id: 11482476
    {'degree': 8, 'field': [-768082, -388100, 391322, -6445, 3226, -7, 7, -4, 1], 'lmfdb_label': '268620.b1', 'torsion': [6]}
  • id: 11482475
    {'degree': 8, 'field': [-246276, -159504, -42296, -17136, -3896, -512, -96, -4, 1], 'lmfdb_label': '268620.b1', 'torsion': [2, 4]}
  • id: 11482474
    {'degree': 8, 'field': [108241, -71722, 23762, -3710, 854, -190, 2, -2, 1], 'lmfdb_label': '268620.b1', 'torsion': [2, 4]}
  • id: 11482478
    {'degree': 16, 'field': [96921, -214896, 65912, -165000, 653436, -930896, 862344, -225944, -93842, 70064, 1512, -7960, 524, 400, -40, -8, 1], 'lmfdb_label': '268620.b1', 'torsion': [8]}
  • id: 11482477
    {'degree': 16, 'field': [37822859361, -1200725694, 19059138, 254726892, -322972916, 2584848, 938448, -1707454, 1063630, -926, -3904, 4240, -1631, 4, 8, -4, 1], 'lmfdb_label': '268620.b1', 'torsion': [4, 4]}
  • id: 11482479
    {'degree': 16, 'field': [724437988272, -547711309272, 168420230108, 30001272140, -3300716692, 2788209680, -383987158, -210579790, 28436219, 996998, -995284, 49260, 4107, -606, 10, -2, 1], 'lmfdb_label': '268620.b1', 'torsion': [2, 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: 6656618
    {'conductor': 268620, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '268620.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6656619
    {'conductor': 268620, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '268620.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6656620
    {'conductor': 268620, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '268620.b1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6656621
    {'conductor': 268620, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '268620.b1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6656622
    {'conductor': 268620, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '268620.b1', 'prime': 37, '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

  
  
  • id: 3362792
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1629, 2376, 0, 1], [1200, 891, 1749, 298], [3249, 8, 3248, 9], [3, 8, 28, 75], [295, 0, 0, 3255], [5, 8, 48, 77], [969, 1782, 1474, 1475]], 'adelic_image': '3256.48.0.?', 'conductor': 268620, 'lmfdb_label': '268620.b1', 'prime': 0}
  • id: 960604
    {'conductor': 268620, 'elladic_image': '4.6.0.3', 'lmfdb_label': '268620.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 268620.b does not appear in ec_padic