Elliptic curve data - 76440.bk4

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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': '76440ci', 'Clabel': '76440ci1', 'Cnumber': 1, 'abc_quality': 0.9775865883163186, 'absD': 1631001175781250000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, -1, 0, -313175, -27735000], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 76440, 'degree': 1032192, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1884098571782444245464181791', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 36, 'isogeny_degrees': [1, 2, 4], 'jinv': [1804588288006144, 866455078125], 'lmfdb_iso': '76440.bk', 'lmfdb_label': '76440.bk4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -6391, 79034], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '42.6.0.a.1', '84.24.0.?', '120.24.0.?', '280.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.6938868768522727716108226991', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.98440572246393933552133110022', 'prec': 103}, 'szpiro_ratio': 4.409107608367991, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 0, 0, 0, 1, 0, 4, 0, 1, 0, -1, 0, 2, 0, 0, 0], 'aplist': [0, -1, 1, 0, 4, 1, 2, 0, 4, -10, 4, 6, 2, -4, 0, -14, -4, 10, -4, 0, 2, 0, -12, 2, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 76440, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '76440.bk', 'trace_hash': 422396537743133732}
• 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': '0.012565256248575025248180091329', 'prec': 107}, 'conductor': 76440, 'gens': [[825, 16575, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.6938868768522727716108226991', 'prec': 100}], 'lmfdb_label': '76440.bk4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.21167279355947114285735558321', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.8426707290782351482282478037120262500', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-275, 6125, 1]], 'xcoord_integral_points': [-275, 600, 825]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [2, 0], '7': 'a', '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '76440.bk4'}
• ec_torsion_growth •

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

  
  
  • id: 3614818
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '76440.bk4', 'torsion': [2, 4]}
  • id: 3614819
    {'degree': 4, 'field': [21, 0, 7, 0, 1], 'lmfdb_label': '76440.bk4', 'torsion': [8]}
  • id: 3614822
    {'degree': 8, 'field': [-164475, -380250, -100350, 29250, 9591, -390, -192, 0, 1], 'lmfdb_label': '76440.bk4', 'torsion': [2, 8]}
  • id: 3614821
    {'degree': 8, 'field': [25, 150, 100, -530, 341, -94, 36, -4, 1], 'lmfdb_label': '76440.bk4', 'torsion': [2, 8]}
  • id: 3614823
    {'degree': 8, 'field': [18460, -3856, 18652, 5052, 1800, -60, -68, -4, 1], 'lmfdb_label': '76440.bk4', 'torsion': [12]}
  • id: 3614820
    {'degree': 8, 'field': [2036329, -1175848, 339488, -119038, 22735, -542, 2, -2, 1], 'lmfdb_label': '76440.bk4', 'torsion': [4, 4]}
  • id: 3614825
    {'degree': 16, 'field': [3515625, 0, 3378072, 0, 1344478, 0, 539664, 0, 11127, 0, -8416, 0, -426, 0, 0, 0, 1], 'lmfdb_label': '76440.bk4', 'torsion': [2, 12]}
  • id: 3614824
    {'degree': 16, 'field': [23140238054336, -19244704587264, 10050018504192, -3638334950656, 815141688704, -110520268544, 10119717888, -986044544, 132459888, -18838016, 2645888, -230048, 12600, -672, 16, -8, 1], 'lmfdb_label': '76440.bk4', 'torsion': [16]}
• 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: 1859230
    {'conductor': 76440, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '76440.bk4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1859231
    {'conductor': 76440, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '76440.bk4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1859232
    {'conductor': 76440, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '76440.bk4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 1859233
    {'conductor': 76440, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '76440.bk4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1859234
    {'conductor': 76440, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '76440.bk4', 'prime': 13, '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: 2168978
    {'adelic_gens': [[833, 8, 832, 9], [1, 0, 8, 1], [113, 108, 110, 527], [1, 8, 0, 1], [1, 4, 4, 17], [592, 837, 475, 838], [337, 8, 508, 33], [7, 6, 834, 835], [739, 738, 538, 115], [284, 1, 583, 6]], 'adelic_image': '840.48.0.?', 'conductor': 76440, 'lmfdb_label': '76440.bk4', 'prime': 0}
  • id: 315685
    {'conductor': 76440, 'elladic_image': '4.12.0.7', 'lmfdb_label': '76440.bk4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 3935355
    {'lmfdb_iso': '76440.bk', 'p': 11, 'prec': 20, 'unit': 7422065747295673289, 'val': 1}
  • id: 3935357
    {'lmfdb_iso': '76440.bk', 'p': 17, 'prec': 20, 'unit': 136351499676929292036843, 'val': 1}
  • id: 3935361
    {'lmfdb_iso': '76440.bk', 'p': 23, 'prec': 20, 'unit': 20122806474784613588923870, 'val': 1}
  • id: 3935356
    {'lmfdb_iso': '76440.bk', 'p': 29, 'prec': 20, 'unit': 4881022550423307661531649089, 'val': 1}
  • id: 3935365
    {'lmfdb_iso': '76440.bk', 'p': 31, 'prec': 20, 'unit': 15792095307299741036435039021, 'val': 1}
  • id: 3935353
    {'lmfdb_iso': '76440.bk', 'p': 37, 'prec': 20, 'unit': 89672405858514790089390764314, 'val': 1}
  • id: 3935354
    {'lmfdb_iso': '76440.bk', 'p': 41, 'prec': 20, 'unit': 1960285387351707502315775252461, 'val': 1}
  • id: 3935352
    {'lmfdb_iso': '76440.bk', 'p': 43, 'prec': 20, 'unit': 8387709672695070454446087464555, 'val': 1}
  • id: 3935359
    {'lmfdb_iso': '76440.bk', 'p': 53, 'prec': 20, 'unit': 75170940140780268876728556427703, 'val': 1}
  • id: 3935363
    {'lmfdb_iso': '76440.bk', 'p': 59, 'prec': 20, 'unit': 2091089964435938720782063806714948, 'val': 1}
  • id: 3935364
    {'lmfdb_iso': '76440.bk', 'p': 61, 'prec': 20, 'unit': 2298832078298404355365426255164833, 'val': 1}
  • id: 3935351
    {'lmfdb_iso': '76440.bk', 'p': 67, 'prec': 20, 'unit': 36308239868435867050640874141398216, 'val': 1}
  • id: 3935360
    {'lmfdb_iso': '76440.bk', 'p': 73, 'prec': 20, 'unit': 202186997029969726153321323691583662, 'val': 1}
  • id: 3935358
    {'lmfdb_iso': '76440.bk', 'p': 83, 'prec': 20, 'unit': 597473573556480970826341393852546965, 'val': 1}
  • id: 3935362
    {'lmfdb_iso': '76440.bk', 'p': 89, 'prec': 20, 'unit': 7557581814399733453131761718018124807, 'val': 1}
  • id: 3935350
    {'lmfdb_iso': '76440.bk', 'p': 97, 'prec': 20, 'unit': 7702551383260843668055345610693101960, 'val': 1}