Elliptic curve data - 247962.bf1

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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': '247962bf', 'Clabel': '247962bf1', 'Cnumber': 1, 'abc_quality': 0.9919278461786771, 'absD': 116166122095104626688, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2244, 'ainvs': [1, 0, 0, -24373688, -46315015104], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 247962, 'degree': 17031168, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9012815455844627942802733749', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2], 'jinv': [66342819962001390625, 4812668669952], 'lmfdb_iso': '247962.bf', 'lmfdb_label': '247962.bf1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -84338, -9461761], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '66.6.0.a.1', '68.6.0.b.1', '2244.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6043387438701960937462666391', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4846748735563547541555060660', 'prec': 100}, 'szpiro_ratio': 5.04311182781191, '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, 0, 1, 4, 1, 1, 0, -1, 1, -1, 4, 0, 1, 0, 1, 2, 0], 'aplist': [1, 1, 0, 4, -1, -1, 0, 2, -4, 2, 0, -10, 2, -6, 6, 2, -10, -8, 0, 0, 4, -8, 12, -2, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 247962, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '247962.bf', 'trace_hash': 182160293804284713}
• 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': '0.0030198047827176676008257543104', 'prec': 110}, 'conductor': 247962, 'gens': [[-2840, 16, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6043387438701960937462666391', 'prec': 100}], 'lmfdb_label': '247962.bf1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.067947132449491568448378475872', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '18.313716476764656049599461200317799275', 'prec': 130}, 'tamagawa_product': 672, 'torsion_generators': [[-2832, 1416, 1]], 'xcoord_integral_points': [-2840, -2832, 9712, 36472]}
• lmfdb_label 247962.bf1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10677008
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '247962.bf1', 'torsion': [2, 2]}
  • id: 10677009
    {'degree': 4, 'field': [26, -34, 11, 0, 1], 'lmfdb_label': '247962.bf1', 'torsion': [4]}
  • id: 10677012
    {'degree': 8, 'field': [-13872, 0, 33983, 0, 408, 0, 0, 0, 1], 'lmfdb_label': '247962.bf1', 'torsion': [6]}
  • id: 10677010
    {'degree': 8, 'field': [1402, -2998, 3535, -2302, 645, -26, 1, -2, 1], 'lmfdb_label': '247962.bf1', 'torsion': [2, 4]}
  • id: 10677011
    {'degree': 8, 'field': [33457152, -3044496, -2217810, 123810, 57799, -224, -438, -2, 1], 'lmfdb_label': '247962.bf1', 'torsion': [2, 4]}
  • id: 10677014
    {'degree': 16, 'field': [84570590592, 18997233696, -18762538248, -437985306, 147351861, 66670056, 10106026, -28048136, 7451676, -320734, 90890, -13464, 1334, 392, -36, -8, 1], 'lmfdb_label': '247962.bf1', 'torsion': [2, 6]}
  • id: 10677013
    {'degree': 16, 'field': [469536866304, 112141860864, -87745892352, -37485026304, 3449938048, 3209771840, 152612592, -94439056, 1205460, 3447528, -71348, -79972, 2157, 862, -74, -6, 1], 'lmfdb_label': '247962.bf1', 'torsion': [8]}
• 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: 6146161
    {'conductor': 247962, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '247962.bf1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 6146162
    {'conductor': 247962, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '247962.bf1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 6146163
    {'conductor': 247962, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '247962.bf1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6146164
    {'conductor': 247962, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '247962.bf1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6146165
    {'conductor': 247962, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '247962.bf1', '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: 3238191
    {'adelic_gens': [[1498, 1, 1495, 0], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [1057, 4, 2114, 9], [818, 1, 1835, 0], [565, 1684, 560, 1683], [2241, 4, 2240, 5]], 'adelic_image': '2244.12.0.?', 'conductor': 247962, 'lmfdb_label': '247962.bf1', 'prime': 0}
  • id: 895435
    {'conductor': 247962, 'elladic_image': '2.3.0.1', 'lmfdb_label': '247962.bf1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 247962.bf does not appear in ec_padic