Elliptic curve data - 39216.i1

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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': '39216i', 'Clabel': '39216i3', 'Cnumber': 3, 'abc_quality': 1.0668830281012522, 'absD': 934289183701204992, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 9804, 'ainvs': [0, -1, 0, -438008, 101568624], 'analytic_rank': 0, 'bad_primes': [2, 3, 19, 43], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 39216, 'degree': 497664, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1843982355564466227813061645', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [2268876641163765625, 228097945239552], 'lmfdb_iso': '39216.i', 'lmfdb_label': '39216.i1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -27376, -1587010], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.48.0-12.j.1.2', '1634.6.0.?', '4902.24.0.?', '9804.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 817], [3, 4, 304], [19, 20, 2064], [43, 44, 912]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4912510549965013133640740430', 'prec': 100}, 'szpiro_ratio': 4.782485333242124, '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, 4, 0, 1, 0, 0, 0, 2, 0, 0, 0, -6, 0, -1, 0], 'aplist': [0, -1, 0, 4, 0, 2, -6, -1, 0, 6, 4, 2, 0, -1, 0, 12, -6, -10, -8, 12, 14, -8, 0, 6, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 39216, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '39216.i', 'trace_hash': 1431539044542376780}
• 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': '0.012666475867709281882639673593', 'prec': 107}, 'conductor': 39216, 'gens': [], 'heights': [], 'lmfdb_label': '39216.i1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.27125792550315226892454753281', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1700634040252181513963802624549525813', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[284, 0, 1]], 'xcoord_integral_points': [284]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '19': [0, 0], '43': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '39216.i1'}
• ec_torsion_growth •

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

  
  
  • id: 1931822
    {'degree': 2, 'field': [-204, -1, 1], 'lmfdb_label': '39216.i1', 'torsion': [2, 2]}
  • id: 1931823
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '39216.i1', 'torsion': [6]}
  • id: 1931824
    {'degree': 4, 'field': [817, 0, 50, 0, 1], 'lmfdb_label': '39216.i1', 'torsion': [4]}
  • id: 1931825
    {'degree': 4, 'field': [40398, 414, -413, -2, 1], 'lmfdb_label': '39216.i1', 'torsion': [2, 6]}
  • id: 1931826
    {'degree': 6, 'field': [29241, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '39216.i1', 'torsion': [6]}
  • id: 1931829
    {'degree': 8, 'field': [2304, 0, -1248, 0, 265, 0, -25, 0, 1], 'lmfdb_label': '39216.i1', 'torsion': [12]}
  • id: 1931828
    {'degree': 8, 'field': [2304, 0, 1200, 0, 673, 0, -25, 0, 1], 'lmfdb_label': '39216.i1', 'torsion': [2, 4]}
  • id: 1931827
    {'degree': 8, 'field': [86307696, 3803696, -3742448, -122076, 59989, 1256, -414, -4, 1], 'lmfdb_label': '39216.i1', 'torsion': [2, 4]}
  • id: 1931830
    {'degree': 12, 'field': [1175056, 0, 385944, 0, 42585, 0, -1147, 0, -336, 0, -3, 0, 1], 'lmfdb_label': '39216.i1', 'torsion': [3, 6]}
  • id: 1931831
    {'degree': 12, 'field': [1364268096, 0, 0, 0, 0, 0, 4521753, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '39216.i1', 'torsion': [2, 6]}
  • id: 1931833
    {'degree': 16, 'field': [-152927171712, 341113421376, 354426056112, 136574600256, 20531342476, -1550164732, -681061554, -511358930, -54959309, 40316924, -329761, -894392, 64582, 3812, -471, -2, 1], 'lmfdb_label': '39216.i1', 'torsion': [2, 12]}
  • id: 1931834
    {'degree': 16, 'field': [5308416, 0, -7190784, 0, 8634721, 0, -1719264, 0, 377904, 0, 29282, 0, 1824, 0, 48, 0, 1], 'lmfdb_label': '39216.i1', 'torsion': [2, 12]}
  • id: 1931832
    {'degree': 16, 'field': [140555258649, 153216242946, 66847596336, 14691398184, 547876869, -117260328, 151429152, 54993006, 21469888, 4276290, 570424, 59496, -2667, -684, -32, -6, 1], 'lmfdb_label': '39216.i1', 'torsion': [8]}
  • id: 1931835
    {'degree': 18, 'field': [49467287324768832, -49688172912413952, -3646852770692736, 2823959930524704, 513855994919040, -34581779289504, -17976457898748, -1247849616096, 167586019200, 34633255176, 875826432, -303244560, -22034736, 1262736, 156816, -2076, -576, 0, 1], 'lmfdb_label': '39216.i1', 'torsion': [18]}
• 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: 926231
    {'conductor': 39216, 'conductor_valuation': 4, 'discriminant_valuation': 36, 'j_denominator_valuation': 24, 'kodaira_symbol': -32, 'lmfdb_label': '39216.i1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 926232
    {'conductor': 39216, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '39216.i1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 926233
    {'conductor': 39216, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '39216.i1', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 926234
    {'conductor': 39216, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '39216.i1', 'prime': 43, '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: 1925613
    {'adelic_gens': [[8266, 3, 5133, 9796], [3269, 12, 3274, 73], [6394, 3, 4305, 9796], [9793, 12, 9792, 13], [1, 12, 0, 1], [1, 6, 6, 37], [1, 0, 12, 1], [5709, 8984, 5746, 8995], [11, 2, 9754, 9795]], 'adelic_image': '9804.96.1.?', 'conductor': 39216, 'lmfdb_label': '39216.i1', 'prime': 0}
  • id: 172263
    {'conductor': 39216, 'elladic_image': '2.3.0.1', 'lmfdb_label': '39216.i1', 'modell_image': '2B', 'prime': 2}
  • id: 172264
    {'conductor': 39216, 'elladic_image': '3.4.0.1', 'lmfdb_label': '39216.i1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 39216.i does not appear in ec_padic