Elliptic curve data - 169756.d2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '169756d', 'Clabel': '169756d2', 'Cnumber': 2, 'abc_quality': 0.887542930342586, 'absD': 1222968887208304, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 6882, 'ainvs': [0, 1, 0, 24186, -849287], 'analytic_rank': 2, 'bad_primes': [2, 31, 37], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 169756, 'degree': 870912, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5830034962292396503480272049', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 3, 'isogeny_degrees': [1, 3], 'jinv': [38112512, 29791], 'lmfdb_iso': '169756.d', 'lmfdb_label': '169756.d2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 18, -11], 'min_quad_twist_disc': 37, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '62.2.0.a.1', '111.8.0.?', '186.8.0.?', '6882.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '6.1278151081813039870426251366', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.45350452027952100830843133777', 'prec': 107}, 'szpiro_ratio': 3.478968691579301, '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, -2, 0, 3, 0, -1, 0, 1, 0, -6, 0, -2, 0, -6, 0, -6, 0, 1, 0], 'aplist': [0, -2, 3, -1, -6, -2, -6, 1, 6, 0, -1, 0, -9, -8, 0, 0, 3, 10, -4, -15, 14, -8, 6, -12, 7], 'class_deg': 3, 'class_size': 2, 'conductor': 169756, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '169756.d', 'trace_hash': 1499285333654777297}
• 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': '0.042171653887759536909403090756', 'prec': 107}, 'conductor': 169756, 'gens': [[86, 1369, 1], [186, 3181, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2403532346748933775833035813', 'prec': 100}, {'__RealLiteral__': 0, 'data': '5.1956981328553457749208895679', 'prec': 100}], 'lmfdb_label': '169756.d2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.27034466707333546308185185430', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.9397328118493785638475291157137163658', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [86, 116, 186]}
• lmfdb_label 169756.d2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7550091
    {'degree': 2, 'field': [28, -1, 1], 'lmfdb_label': '169756.d2', 'torsion': [3]}
  • id: 7550092
    {'degree': 3, 'field': [-1, 1, 0, 1], 'lmfdb_label': '169756.d2', 'torsion': [2]}
  • id: 7550094
    {'degree': 6, 'field': [-669, -357, 222, 49, -24, -3, 1], 'lmfdb_label': '169756.d2', 'torsion': [3]}
  • id: 7550093
    {'degree': 6, 'field': [1, -3, 7, -9, 7, -3, 1], 'lmfdb_label': '169756.d2', 'torsion': [2, 2]}
  • id: 7550095
    {'degree': 6, 'field': [21981, -951, 2323, -53, 83, -1, 1], 'lmfdb_label': '169756.d2', 'torsion': [6]}
  • id: 7550096
    {'degree': 12, 'field': [-1414319624, 113799168, 111686248, -8587256, -3049336, 8208, 54896, 1144, -2046, 328, 38, -2, 1], 'lmfdb_label': '169756.d2', 'torsion': [4]}
  • id: 7550097
    {'degree': 12, 'field': [264196, 0, -253728, 0, 97500, 0, -17321, 0, 1515, 0, -63, 0, 1], 'lmfdb_label': '169756.d2', 'torsion': [3, 3]}
  • id: 7550098
    {'degree': 12, 'field': [357172201, 0, 87875093, 0, 8647473, 0, 438313, 0, 12105, 0, 173, 0, 1], 'lmfdb_label': '169756.d2', 'torsion': [2, 6]}
  • id: 7550100
    {'degree': 18, 'field': [-306526621, -472821423, 38597919, 335050086, 25399848, -115986198, -8041466, 23825574, 913419, -3160287, -17097, 277998, -7000, -15984, 864, 552, -45, -9, 1], 'lmfdb_label': '169756.d2', 'torsion': [6]}
  • id: 7550099
    {'degree': 18, 'field': [59736514799493, -19910570359653, 13574297842272, -3098377084086, 1280386931841, -232896789423, 74812935858, -11320559379, 3005260542, -378895503, 86314998, -9037851, 1785550, -149595, 25545, -1606, 234, -9, 1], 'lmfdb_label': '169756.d2', 'torsion': [9]}
• 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: 4200539
    {'conductor': 169756, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '169756.d2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 4200540
    {'conductor': 169756, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '169756.d2', 'prime': 31, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4200541
    {'conductor': 169756, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '169756.d2', 'prime': 37, '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: 2759457
    {'adelic_gens': [[4, 3, 9, 7], [6695, 0, 0, 6881], [5366, 777, 1591, 5773], [4219, 5772, 5217, 3553], [1, 6, 0, 1], [3, 4, 8, 11], [6877, 6, 6876, 7], [1, 0, 6, 1]], 'adelic_image': '6882.16.0.?', 'conductor': 169756, 'lmfdb_label': '169756.d2', 'prime': 0}
  • id: 641408
    {'conductor': 169756, 'elladic_image': '3.4.0.1', 'lmfdb_label': '169756.d2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 169756.d does not appear in ec_padic