Elliptic curve data - 345576.bc1

Formats: - HTML - YAML - JSON - 2024-06-09T04:09:53.250912

• 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': '345576bc', 'Clabel': '345576bc3', 'Cnumber': 3, 'abc_quality': 0.9500550123380991, 'absD': 3181786595226624, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 31416, 'ainvs': [0, 1, 0, -65864, 5891136], 'analytic_rank': 2, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 345576, 'degree': 1638400, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7108210683397510190274020954', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2, 4], 'jinv': [17418812548, 1753941], 'lmfdb_iso': '345576.bc', 'lmfdb_label': '345576.bc1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -544, -4624], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '42.6.0.a.1', '44.12.0-4.c.1.1', '84.12.0.?', '136.12.0.?', '924.24.0.?', '1496.24.0.?', '2856.24.0.?', '31416.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '17.231085054577902969086350500', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.065749218526055344184596461464', 'prec': 110}, 'szpiro_ratio': 3.520722434451155, '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, -2, 0, -1, 0, 1, 0, 0, 0, -6, 0, -2, 0, -1, 0, 0, 0], 'aplist': [0, 1, -2, -1, 0, -6, -1, 0, 0, -2, 0, 6, -2, -4, 0, -2, -4, -2, 4, 0, -14, -8, -12, -6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 345576, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '345576.bc', 'trace_hash': 2280609842755397442}
• 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': '0.032658760731984228910695548989', 'prec': 107}, 'conductor': 345576, 'gens': [[192, 600, 1], [4672, 285560, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '4.2482795570866711214142226136', 'prec': 100}, {'__RealLiteral__': 0, 'data': '5.0682349779369686218210083872', 'prec': 100}], 'lmfdb_label': '345576.bc1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.43552547302592005768249359478', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '15.009152938289805449012099431981724089', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[183, 0, 1]], 'xcoord_integral_points': [183, 192]}
• lmfdb_label 345576.bc1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 14433642
    {'degree': 2, 'field': [-231, 0, 1], 'lmfdb_label': '345576.bc1', 'torsion': [4]}
  • id: 14433643
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '345576.bc1', 'torsion': [4]}
  • id: 14433641
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '345576.bc1', 'torsion': [2, 2]}
  • id: 14433644
    {'degree': 4, 'field': [25, 32, -31, -2, 1], 'lmfdb_label': '345576.bc1', 'torsion': [2, 4]}
  • id: 14433648
    {'degree': 8, 'field': [-43923, 0, 101156, 0, -726, 0, 0, 0, 1], 'lmfdb_label': '345576.bc1', 'torsion': [6]}
  • id: 14433647
    {'degree': 8, 'field': [77, -110, 170, -106, 19, 38, -8, -4, 1], 'lmfdb_label': '345576.bc1', 'torsion': [8]}
  • id: 14433645
    {'degree': 8, 'field': [6549, -2796, 2682, 216, -77, -40, 18, -4, 1], 'lmfdb_label': '345576.bc1', 'torsion': [2, 4]}
  • id: 14433646
    {'degree': 8, 'field': [66049, 0, -153730, 0, 31071, 0, -502, 0, 1], 'lmfdb_label': '345576.bc1', 'torsion': [8]}
  • id: 14433653
    {'degree': 16, 'field': [-4039086399, 21715284468, -22592951352, -10778937840, 20289389040, -8771822388, 1719645664, -138506480, 4200342, -2119428, 717888, -55608, -4020, 324, 24, -8, 1], 'lmfdb_label': '345576.bc1', 'torsion': [12]}
  • id: 14433651
    {'degree': 16, 'field': [-131121392, 373094112, 727452512, -1900717168, 229091780, 783770472, -128985796, -105509064, 16748041, 6105360, -911048, -163904, 23010, 1960, -260, -8, 1], 'lmfdb_label': '345576.bc1', 'torsion': [2, 8]}
  • id: 14433649
    {'degree': 16, 'field': [447561, 0, 944280, 0, 627090, 0, 96900, 0, -9629, 0, -620, 0, 270, 0, -20, 0, 1], 'lmfdb_label': '345576.bc1', 'torsion': [4, 4]}
  • id: 14433650
    {'degree': 16, 'field': [1004004, 0, -216960, 0, 820156, 0, -492228, 0, 148341, 0, -23116, 0, 1926, 0, -72, 0, 1], 'lmfdb_label': '345576.bc1', 'torsion': [2, 8]}
  • id: 14433654
    {'degree': 16, 'field': [217503504, 0, -131262048, 0, 49749264, 0, -9727904, 0, 1071320, 0, -74648, 0, 3376, 0, -88, 0, 1], 'lmfdb_label': '345576.bc1', 'torsion': [12]}
  • id: 14433652
    {'degree': 16, 'field': [192347781201, 103695510888, -93286552716, -20577974520, 9704336298, 658833192, -147831548, -62588720, 16970919, -873568, 165236, 5856, -1522, 224, -12, -8, 1], 'lmfdb_label': '345576.bc1', '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: 8551619
    {'conductor': 345576, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '345576.bc1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8551620
    {'conductor': 345576, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '345576.bc1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 8551621
    {'conductor': 345576, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '345576.bc1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 8551622
    {'conductor': 345576, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '345576.bc1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8551623
    {'conductor': 345576, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '345576.bc1', '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: 3821973
    {'adelic_gens': [[7, 6, 31410, 31411], [1, 8, 0, 1], [30196, 8569, 26543, 11430], [1, 0, 8, 1], [5545, 5720, 25036, 22881], [29635, 12496, 28226, 15357], [15236, 8569, 19063, 11430], [1, 4, 4, 17], [8567, 0, 0, 31415], [29635, 29634, 28930, 10363], [31409, 8, 31408, 9]], 'adelic_image': '31416.48.0.?', 'conductor': 345576, 'lmfdb_label': '345576.bc1', 'prime': 0}
  • id: 1196852
    {'conductor': 345576, 'elladic_image': '4.6.0.1', 'lmfdb_label': '345576.bc1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 345576.bc does not appear in ec_padic