Elliptic curve data - 16576.d1

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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': '16576f', 'Clabel': '16576f2', 'Cnumber': 2, 'abc_quality': 0.8893097731815562, 'absD': 570558119936, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2072, 'ainvs': [0, 1, 0, -5857, -170625], 'analytic_rank': 0, 'bad_primes': [2, 7, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 16576, 'degree': 27648, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0380643464148087134196257737', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2], 'jinv': [169556172914, 4353013], 'lmfdb_iso': '16576.d', 'lmfdb_label': '16576.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1464, -20596], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '296.6.0.?', '2072.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 37], [3, 2, 2368], [7, 8, 2368], [37, 38, 448]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.056105840621552858411880268301', 'prec': 107}, 'szpiro_ratio': 3.8741324870642773, '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, -2, 0, 2, 0, -1, 0, 1, 0, -4, 0, 6, 0, -4, 0, -4, 0, -4, 0], 'aplist': [0, -2, 2, -1, -4, 6, -4, -4, 0, 10, 2, 1, -2, 4, 0, -6, 0, 14, -12, -8, -14, 12, -6, 0, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 16576, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '16576.d', 'trace_hash': 1284287802614852913}
• 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': '0.12541479279984093977712200033', 'prec': 103}, 'conductor': 16576, 'gens': [], 'heights': [], 'lmfdb_label': '16576.d1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.54658120395922651806886959923', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0931624079184530361377391984658129762', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-39, 0, 1]], 'xcoord_integral_points': [-39]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '7': [0, 0], '37': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '16576.d1'}
• ec_torsion_growth •

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

  
  
  • id: 848955
    {'degree': 2, 'field': [-74, 0, 1], 'lmfdb_label': '16576.d1', 'torsion': [2, 2]}
  • id: 848956
    {'degree': 4, 'field': [74, 0, 11, 0, 1], 'lmfdb_label': '16576.d1', 'torsion': [4]}
  • id: 848959
    {'degree': 8, 'field': [-147, 0, 134, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '16576.d1', 'torsion': [6]}
  • id: 848958
    {'degree': 8, 'field': [-74, 592, -1776, 2368, -1183, -4, 6, -4, 1], 'lmfdb_label': '16576.d1', 'torsion': [2, 4]}
  • id: 848957
    {'degree': 8, 'field': [43688, 2320, -2052, -588, 425, -160, 58, -4, 1], 'lmfdb_label': '16576.d1', 'torsion': [2, 4]}
  • id: 848960
    {'degree': 16, 'field': [16676, -795368, 9265126, 11409880, 5235418, 1586436, 1004027, 238146, -32015, -4632, 2400, -132, -344, 28, 7, -6, 1], 'lmfdb_label': '16576.d1', 'torsion': [8]}
  • id: 848961
    {'degree': 16, 'field': [1205604, 0, -3866616, 0, 3210300, 0, -845640, 0, 36216, 0, 9756, 0, 868, 0, -10, 0, 1], 'lmfdb_label': '16576.d1', '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: 368189
    {'conductor': 16576, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '16576.d1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 368190
    {'conductor': 16576, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '16576.d1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 368191
    {'conductor': 16576, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '16576.d1', '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: 1774317
    {'adelic_gens': [[1, 2, 2, 5], [2, 1, 1035, 0], [1, 4, 0, 1], [297, 4, 594, 9], [226, 1, 1959, 0], [1297, 778, 776, 1295], [2069, 4, 2068, 5], [1, 0, 4, 1], [3, 4, 8, 11]], 'adelic_image': '2072.12.0.?', 'conductor': 16576, 'lmfdb_label': '16576.d1', 'prime': 0}
  • id: 77795
    {'conductor': 16576, 'elladic_image': '2.3.0.1', 'lmfdb_label': '16576.d1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 16576.d does not appear in ec_padic