Elliptic curve data - 178752.a2

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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': '178752cw', 'Clabel': '178752cw1', 'Cnumber': 1, 'abc_quality': 0.9637314115206085, 'absD': 257209244661445558272, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1596, 'ainvs': [0, -1, 0, -3183105, 2046212001], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 178752, 'degree': 12386304, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6630205224294545647431521141', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [115650783909361, 8339853312], 'lmfdb_iso': '178752.a', 'lmfdb_label': '178752.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1015, 11561], 'min_quad_twist_disc': 56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.b.1', '114.6.0.?', '1596.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 2793], [3, 4, 59584], [7, 32, 1216], [19, 20, 9408]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.65034467706187994806462756019', 'prec': 103}, 'szpiro_ratio': 4.674619922981036, '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, -4, 0, 0, 0, 1, 0, -6, 0, -4, 0, 4, 0, 4, 0, 1, 0], 'aplist': [0, -1, -4, 0, -6, -4, 4, 1, -2, -2, 4, -2, -6, 0, -8, 14, 4, -10, 10, 4, 14, -2, 0, -6, 0], 'class_deg': 2, 'class_size': 2, 'conductor': 178752, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '178752.a', 'trace_hash': 102785832961965478}
• 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': '0.0048632854796169099543358818531', 'prec': 110}, 'conductor': 178752, 'gens': [], 'heights': [], 'lmfdb_label': '178752.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.17132931786893653485959710937', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.68531727147574613943838843747893219390', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[1237, 0, 1]], 'xcoord_integral_points': [1237]}
• lmfdb_label 178752.a2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7914364
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '178752.a2', 'torsion': [2, 2]}
  • id: 7914365
    {'degree': 4, 'field': [57, 0, -40, 0, 1], 'lmfdb_label': '178752.a2', 'torsion': [4]}
  • id: 7914368
    {'degree': 8, 'field': [-37632, 0, -14840, 0, -672, 0, 0, 0, 1], 'lmfdb_label': '178752.a2', 'torsion': [6]}
  • id: 7914367
    {'degree': 8, 'field': [36, 0, -492, 0, 325, 0, -44, 0, 1], 'lmfdb_label': '178752.a2', 'torsion': [2, 4]}
  • id: 7914366
    {'degree': 8, 'field': [60592, -32144, 34430, -4568, 2275, 8, 2, -4, 1], 'lmfdb_label': '178752.a2', 'torsion': [2, 4]}
  • id: 7914369
    {'degree': 16, 'field': [-156016, 598976, -105056, 296352, 777728, 256256, -171696, -148624, -3288, -10000, 840, 3752, -224, 0, -28, -4, 1], 'lmfdb_label': '178752.a2', 'torsion': [8]}
  • id: 7914370
    {'degree': 16, 'field': [110010555424, 33748385440, -31971563064, -3462658752, 1505984928, 264699456, -79376864, -6270320, -54711, 1037784, -165396, -21000, 1862, 728, -84, -8, 1], 'lmfdb_label': '178752.a2', '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: 4423524
    {'conductor': 178752, 'conductor_valuation': 6, 'discriminant_valuation': 30, 'j_denominator_valuation': 12, 'kodaira_symbol': -24, 'lmfdb_label': '178752.a2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4423525
    {'conductor': 178752, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '178752.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4423526
    {'conductor': 178752, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '178752.a2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4423527
    {'conductor': 178752, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '178752.a2', 'prime': 19, '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: 2814679
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [913, 4, 230, 9], [1, 4, 0, 1], [1066, 1, 1063, 0], [1593, 4, 1592, 5], [422, 1, 587, 0], [1201, 400, 1196, 399]], 'adelic_image': '1596.12.0.?', 'conductor': 178752, 'lmfdb_label': '178752.a2', 'prime': 0}
  • id: 671249
    {'conductor': 178752, 'elladic_image': '2.3.0.1', 'lmfdb_label': '178752.a2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 178752.a does not appear in ec_padic