Elliptic curve data - 42978.b1

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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': '42978a', 'Clabel': '42978a1', 'Cnumber': 1, 'abc_quality': 0.8755530539992665, 'absD': 29750403072, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 171912, 'ainvs': [1, 1, 0, 321, 8133], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 19, 29], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 42978, 'degree': 43680, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.69108050342108689353824660664', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [3640182186887, 29750403072], 'lmfdb_iso': '42978.b', 'lmfdb_label': '42978.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 321, 8133], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['171912.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7290861933814390093022976780', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 21489], [3, 4, 1102], [13, 14, 1653], [19, 20, 2262], [29, 30, 1482]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.69108050342108689353824660664', 'prec': 103}, 'szpiro_ratio': 2.9523882693035923, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 6, -1, 1, 1, -2, 1, -3, -1, -1, 2], 'aplist': [-1, -1, 2, -1, 6, 1, -3, -1, 0, 1, -7, 5, 10, -8, 3, 0, 12, -10, -7, -3, -6, 6, 3, -5, -12], 'class_deg': 1, 'class_size': 1, 'conductor': 42978, 'isogeny_matrix': [[1]], 'lmfdb_iso': '42978.b', 'trace_hash': 1370513879753721239}
• 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': '0.25103547709203603889064659113', 'prec': 103}, 'conductor': 42978, 'gens': [[-11, 64, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7290861933814390093022976780', 'prec': 100}], 'lmfdb_label': '42978.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.85995490900818078677282930828', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.4608084802899112129805126266570620466', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': [-11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [1, 0], '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [2, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '42978.b1'}
• ec_torsion_growth •

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

  
  
  • id: 2106112
    {'degree': 3, 'field': [-432, 66, 0, 1], 'lmfdb_label': '42978.b1', 'torsion': [2]}
  • id: 2106113
    {'degree': 6, 'field': [694048, -330704, 49862, 4, -163, -2, 1], 'lmfdb_label': '42978.b1', 'torsion': [2, 2]}
  • id: 2106114
    {'degree': 8, 'field': [-147, 0, 220, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '42978.b1', 'torsion': [3]}
  • id: 2106115
    {'degree': 12, 'field': [17817276240, -3982376072, -3903618115, -159129852, 109668507, -8752108, 2760769, -585536, 39125, -804, -33, -4, 1], 'lmfdb_label': '42978.b1', 'torsion': [4]}
• 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: 1020306
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 13, 'j_denominator_valuation': 13, 'kodaira_symbol': 17, 'lmfdb_label': '42978.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1020307
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42978.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1020308
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '42978.b1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1020309
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42978.b1', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1020310
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42978.b1', 'prime': 29, '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

  
  {'adelic_gens': [[171911, 2, 171910, 3], [57305, 2, 57305, 3], [1, 2, 0, 1], [1, 0, 2, 1], [100777, 2, 100777, 3], [119017, 2, 119017, 3], [128935, 2, 128935, 3], [45241, 2, 45241, 3], [1, 1, 171911, 0], [85957, 2, 85957, 3]], 'adelic_image': '171912.2.0.?', 'conductor': 42978, 'lmfdb_label': '42978.b1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2139762
    {'lmfdb_iso': '42978.b', 'p': 5, 'prec': 20, 'unit': 644227941836, 'val': 3}
  • id: 2139749
    {'lmfdb_iso': '42978.b', 'p': 7, 'prec': 20, 'unit': 7058227010793846, 'val': 1}
  • id: 2139747
    {'lmfdb_iso': '42978.b', 'p': 11, 'prec': 20, 'unit': 43596417846683389098, 'val': 1}
  • id: 2139754
    {'lmfdb_iso': '42978.b', 'p': 17, 'prec': 20, 'unit': 81115367723708867015326, 'val': 1}
  • id: 2139750
    {'lmfdb_iso': '42978.b', 'p': 31, 'prec': 20, 'unit': 4495657690009028586896707923, 'val': 1}
  • id: 2139748
    {'lmfdb_iso': '42978.b', 'p': 37, 'prec': 20, 'unit': 465241452015916662936235193247, 'val': 1}
  • id: 2139751
    {'lmfdb_iso': '42978.b', 'p': 41, 'prec': 20, 'unit': 2995955659458619542535966520953, 'val': 1}
  • id: 2139752
    {'lmfdb_iso': '42978.b', 'p': 43, 'prec': 20, 'unit': 1800945252760415014865444098332, 'val': 1}
  • id: 2139760
    {'lmfdb_iso': '42978.b', 'p': 47, 'prec': 20, 'unit': 1895682356366962007722048654886, 'val': 1}
  • id: 2139756
    {'lmfdb_iso': '42978.b', 'p': 59, 'prec': 20, 'unit': 607684227914534686277252701366578, 'val': 1}
  • id: 2139761
    {'lmfdb_iso': '42978.b', 'p': 61, 'prec': 20, 'unit': 5472906615385602996216296961824228, 'val': 1}
  • id: 2139746
    {'lmfdb_iso': '42978.b', 'p': 67, 'prec': 20, 'unit': 16742914433504563260444227649857603, 'val': 1}
  • id: 2139759
    {'lmfdb_iso': '42978.b', 'p': 71, 'prec': 20, 'unit': 55018425724211947913307682636009079, 'val': 1}
  • id: 2139757
    {'lmfdb_iso': '42978.b', 'p': 73, 'prec': 20, 'unit': 20589758086659728400685794829008842, 'val': 1}
  • id: 2139753
    {'lmfdb_iso': '42978.b', 'p': 79, 'prec': 20, 'unit': 517795896854746219913271004095222490, 'val': 1}
  • id: 2139755
    {'lmfdb_iso': '42978.b', 'p': 83, 'prec': 20, 'unit': 1486111145055159793023073160509357755, 'val': 1}
  • id: 2139758
    {'lmfdb_iso': '42978.b', 'p': 89, 'prec': 20, 'unit': 1544508163191342164655823483466070056, 'val': 1}
  • id: 2139745
    {'lmfdb_iso': '42978.b', 'p': 97, 'prec': 20, 'unit': 11198699841008124279873105645584450941, 'val': 1}