Elliptic curve data - 86700.p2

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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': '86700c', 'Clabel': '86700c2', 'Cnumber': 2, 'abc_quality': 0.8671697888311541, 'absD': 6278181696900000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2040, 'ainvs': [0, -1, 0, 142092, -118823688], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 86700, 'degree': 1990656, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2873394318855763917040133893', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [3286064, 65025], 'lmfdb_iso': '86700.p', 'lmfdb_label': '86700.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 20, -200], 'min_quad_twist_disc': 85, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '24.12.0-4.a.1.2', '340.12.0.?', '680.24.0.?', '2040.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 7225], [3, 4, 28900], [5, 18, 3468], [17, 162, 300]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.39608431673287870866595500056', 'prec': 107}, 'szpiro_ratio': 4.459781708247133, '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, 0, 0, 0, 0, 1, 0, 6, 0, -2, 0, 0, 0, 0, 0, -8, 0], 'aplist': [0, -1, 0, 0, 6, -2, 0, -8, -4, -6, -10, -6, 10, 2, 6, 10, 0, -2, 10, -14, -6, -10, 14, -10, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 86700, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '86700.p', 'trace_hash': 1968324182024185448}
• 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': '0.010309609435545500743749091224', 'prec': 107}, 'conductor': 86700, 'gens': [], 'heights': [], 'lmfdb_label': '86700.p2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.11585086147986713229467903656', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.92680689183893705835743229250641776331', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[397, 0, 1]], 'xcoord_integral_points': [397]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': 'a', '17': 'a'}, 'iwp0': 3, 'lmfdb_label': '86700.p2'}
• ec_torsion_growth •

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

  
  
  • id: 4061714
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '86700.p2', 'torsion': [2, 2]}
  • id: 4061715
    {'degree': 4, 'field': [-9, 0, -7, 0, 1], 'lmfdb_label': '86700.p2', 'torsion': [4]}
  • id: 4061718
    {'degree': 8, 'field': [-14646, 6264, -1070, 297, 120, -63, 27, 0, 1], 'lmfdb_label': '86700.p2', 'torsion': [6]}
  • id: 4061716
    {'degree': 8, 'field': [225, -150, 50, -90, 39, 2, 8, -4, 1], 'lmfdb_label': '86700.p2', 'torsion': [2, 4]}
  • id: 4061717
    {'degree': 8, 'field': [574600, 47600, -77800, -4320, 3584, 72, -52, -4, 1], 'lmfdb_label': '86700.p2', 'torsion': [2, 4]}
  • id: 4061719
    {'degree': 16, 'field': [585225, 0, -771120, 0, 328986, 0, -57708, 0, 14299, 0, -364, 0, 294, 0, -28, 0, 1], 'lmfdb_label': '86700.p2', 'torsion': [4, 4]}
  • id: 4061720
    {'degree': 16, 'field': [585225, 0, 0, 0, -350370, 0, 128520, 0, -43949, 0, 3304, 0, 326, 0, -56, 0, 1], 'lmfdb_label': '86700.p2', 'torsion': [8]}
  • id: 4061721
    {'degree': 16, 'field': [1185921, 1019304, 438048, 337968, -192924, -26316, 96800, -26696, 3874, -3072, 4360, -1768, 416, -84, 32, -8, 1], 'lmfdb_label': '86700.p2', '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: 2116179
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '86700.p2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2116180
    {'conductor': 86700, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '86700.p2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2116181
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '86700.p2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2116182
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '86700.p2', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2235143
    {'adelic_gens': [[1021, 8, 2, 17], [1531, 4, 767, 9], [1, 0, 8, 1], [5, 8, 48, 77], [1799, 2038, 0, 2039], [2033, 8, 2032, 9], [3, 8, 10, 27], [1361, 8, 682, 17], [1223, 2034, 0, 2039], [1, 8, 0, 1]], 'adelic_image': '2040.48.0.?', 'conductor': 86700, 'lmfdb_label': '86700.p2', 'prime': 0}
  • id: 353389
    {'conductor': 86700, 'elladic_image': '4.6.0.5', 'lmfdb_label': '86700.p2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 86700.p does not appear in ec_padic