Elliptic curve data - 86394.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': '86394b', 'Clabel': '86394b6', 'Cnumber': 6, 'abc_quality': 1.0624727966937526, 'absD': 31783636615224993056712, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2992, 'ainvs': [1, 1, 0, -1659951086, 26030318798796], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 86394, 'degree': 39321600, 'elladic_images': ['8.48.0.217'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7780766057222030345657789101', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [285531136548675601769470657, 17941034271597192], 'lmfdb_iso': '86394.d', 'lmfdb_label': '86394.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -13718604, -19563199515], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0.p.1', '44.12.0-4.c.1.1', '88.96.0.?', '272.96.1.?', '2992.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 121], [3, 4, 14399], [7, 8, 12342], [11, 62, 714], [17, 18, 5082]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.5791289693230177625348071211', 'prec': 100}, 'szpiro_ratio': 6.624960671117553, '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, -1, -1, 1, -2, 1, -1, -1, 1, 2, 0, -1, 2, 1, 2, 1, -1, -1, -4, -2], 'aplist': [-1, -1, -2, -1, 0, 2, -1, -4, 8, -6, 0, -2, -10, 4, 0, 6, -4, -6, -12, -8, 6, 0, 12, -6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 86394, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '86394.d', 'trace_hash': 1640888170793253405}
• 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': '0.00052288279965775336527009430984', 'prec': 113}, 'conductor': 86394, 'gens': [], 'heights': [], 'lmfdb_label': '86394.d1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.088427757911417052754713057722', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.35371103164566821101885223088800551515', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[94107, -94107, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [7, 0], '3': [0, 0], '7': [0, 0], '11': 'a', '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '86394.d1'}
• ec_torsion_growth •

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

  
  
  • id: 4046242
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '86394.d1', 'torsion': [4]}
  • id: 4046241
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '86394.d1', 'torsion': [8]}
  • id: 4046240
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '86394.d1', 'torsion': [2, 2]}
  • id: 4046243
    {'degree': 4, 'field': [25, 0, -12, 0, 1], 'lmfdb_label': '86394.d1', 'torsion': [2, 8]}
  • id: 4046247
    {'degree': 8, 'field': [-239744, 165436, -36446, 5435, -1750, 311, -17, -2, 1], 'lmfdb_label': '86394.d1', 'torsion': [6]}
  • id: 4046246
    {'degree': 8, 'field': [1721, -272, 2792, -816, 141, -68, 2, 0, 1], 'lmfdb_label': '86394.d1', 'torsion': [16]}
  • id: 4046244
    {'degree': 8, 'field': [8999, -3244, 3102, 272, -105, -40, 18, -4, 1], 'lmfdb_label': '86394.d1', 'torsion': [2, 4]}
  • id: 4046245
    {'degree': 8, 'field': [10371, 3028, -2778, -512, 287, -40, 18, -4, 1], 'lmfdb_label': '86394.d1', 'torsion': [8]}
  • id: 4046253
    {'degree': 16, 'field': [4624, 0, -117307, 0, -11294, 0, 10515, 0, -2781, 0, -1041, 0, 247, 0, -22, 0, 1], 'lmfdb_label': '86394.d1', 'torsion': [24]}
  • id: 4046250
    {'degree': 16, 'field': [24777, -29292, 34436, -10860, 10340, -14240, 14784, -1804, -5995, 1320, 2332, -948, -206, 140, 0, -8, 1], 'lmfdb_label': '86394.d1', 'torsion': [2, 16]}
  • id: 4046249
    {'degree': 16, 'field': [204521, -277784, -71852, 626080, -125174, -240632, 110320, -36200, 23955, -13112, 6160, -2408, 826, -224, 52, -8, 1], 'lmfdb_label': '86394.d1', 'torsion': [2, 8]}
  • id: 4046248
    {'degree': 16, 'field': [266121, 2126184, 3800240, -13783224, 12084128, -7299656, 4343640, -1904752, 829697, -266568, 85372, -18984, 4438, -616, 108, -8, 1], 'lmfdb_label': '86394.d1', 'torsion': [4, 8]}
  • id: 4046254
    {'degree': 16, 'field': [1183744, 0, -15015296, 0, -722816, 0, 336480, 0, -44496, 0, -8328, 0, 988, 0, -44, 0, 1], 'lmfdb_label': '86394.d1', 'torsion': [12]}
  • id: 4046251
    {'degree': 16, 'field': [96173361, 147136584, -1927333960, 782723312, 1424545496, -451697736, -369211128, 62767712, 38951902, -2816296, -1753848, 49392, 36216, -280, -328, 0, 1], 'lmfdb_label': '86394.d1', 'torsion': [2, 16]}
  • id: 4046252
    {'degree': 16, 'field': [39207257224, -68609508752, 47828563676, -17959008512, 4696628022, -1125194996, 203480745, -23543456, 3422980, -559954, 52737, 3656, -4059, 746, -46, -4, 1], 'lmfdb_label': '86394.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: 2107473
    {'conductor': 86394, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '86394.d1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2107474
    {'conductor': 86394, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '86394.d1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2107475
    {'conductor': 86394, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '86394.d1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2107476
    {'conductor': 86394, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '86394.d1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2107477
    {'conductor': 86394, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '86394.d1', 'prime': 17, 'reduction_type': -1, '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: 2232935
    {'adelic_gens': [[5, 4, 2988, 2989], [727, 2464, 1342, 2201], [2977, 16, 2976, 17], [1, 16, 0, 1], [1057, 2464, 2200, 1761], [15, 2, 2894, 2979], [1, 0, 16, 1], [892, 1705, 1771, 2586], [1087, 0, 0, 2991]], 'adelic_image': '2992.192.1.?', 'conductor': 86394, 'lmfdb_label': '86394.d1', 'prime': 0}
  • id: 352068
    {'conductor': 86394, 'elladic_image': '8.48.0.217', 'lmfdb_label': '86394.d1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 86394.d does not appear in ec_padic