Elliptic curve data - 256.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': '256a', 'Clabel': '256a1', 'Cnumber': 1, 'abc_quality': 0.9029767420170889, 'absD': 512, 'ainvs': [0, 1, 0, -3, 1], 'analytic_rank': 1, 'bad_primes': [2], 'class_deg': 2, 'class_size': 2, 'cm': -8, 'conductor': 256, 'degree': 8, 'elladic_images': ['16.192.5.607'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.75054624063986677446489366634', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [8000, 1], 'lmfdb_iso': '256.a', 'lmfdb_label': '256.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -3, 1], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 1, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.48012579750829764693652026591', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 1]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2704066260598257565278177574', 'prec': 103}, 'szpiro_ratio': 2.745723035582761, '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, -2, 0, 0, 0, 0, 0, 1, 0, -6, 0, 0, 0, 0, 0, -6, 0, -2, 0], 'aplist': [0, -2, 0, 0, -6, 0, -6, -2, 0, 0, 0, 0, 6, 10, 0, 0, -6, 0, 14, 0, -2, 0, -18, -18, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 256, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '256.a', 'trace_hash': 482854227665579260}
• 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': '4.4865879072055443003307712123', 'prec': 100}, 'conductor': 256, 'gens': [[0, 1, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.48012579750829764693652026591', 'prec': 103}], 'lmfdb_label': '256.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '5.0378540936193068771615222380', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2094018572147058551904833617186879585', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[1, 0, 1]], 'xcoord_integral_points': [-1, 0, 1, 9]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 1, 0], '7': [3, 1, 0], '11': [1, 0], '13': [1, 1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 1, 0], '31': [1, 1, 0], '37': [1, 1, 0], '41': [1, 0], '43': [1, 0], '47': [3, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '256.a2'}
• ec_torsion_growth •

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

  
  
  • id: 10987
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [2, 2]}
  • id: 10990
    {'degree': 4, 'field': [-2, 0, 4, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [6]}
  • id: 10988
    {'degree': 4, 'field': [2, 0, -4, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [2, 4]}
  • id: 10989
    {'degree': 4, 'field': [6, 0, -4, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [6]}
  • id: 10992
    {'degree': 8, 'field': [1, 0, -4, 0, -2, 0, -4, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [2, 8]}
  • id: 10995
    {'degree': 8, 'field': [1, 0, 0, 0, -4, 0, 0, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [2, 6]}
  • id: 10991
    {'degree': 8, 'field': [1, 0, 4, 0, -2, 0, 4, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [2, 4]}
  • id: 10994
    {'degree': 8, 'field': [9, 0, -24, 0, 16, 0, 0, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [2, 6]}
  • id: 10993
    {'degree': 8, 'field': [36, 0, 24, 0, 10, 0, 4, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [3, 6]}
  • id: 10996
    {'degree': 12, 'field': [24, 0, 0, 0, 24, 0, 8, 0, 6, 0, 4, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [18]}
  • id: 10997
    {'degree': 16, 'field': [1, -8, 36, -104, 220, -368, 516, -624, 664, -624, 516, -368, 220, -104, 36, -8, 1], 'lmfdb_label': '256.a2', 'torsion': [4, 8]}
  • id: 10998
    {'degree': 16, 'field': [1, 0, 0, 0, -4, 0, 0, 0, 15, 0, 0, 0, -4, 0, 0, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [6, 6]}
  • id: 11000
    {'degree': 16, 'field': [4, 0, -48, 0, 152, 0, -224, 0, 192, 0, -104, 0, 36, 0, -8, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [2, 12]}
  • id: 10999
    {'degree': 16, 'field': [4, 0, -16, 0, 24, 0, 0, 0, -24, 0, 24, 0, 12, 0, -8, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [2, 12]}
  • id: 11001
    {'degree': 20, 'field': [352, 0, 704, 0, 528, 0, 352, 0, 352, 0, 160, 0, 92, 0, 40, 0, 18, 0, 4, 0, 1], 'lmfdb_label': '256.a2', 'torsion': [22]}
• 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

  
  {'conductor': 256, 'conductor_valuation': 8, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '256.a2', 'prime': 2, 'reduction_type': 0, '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

  
  {'conductor': 256, 'elladic_image': '16.192.5.607', 'lmfdb_label': '256.a2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2411
    {'lmfdb_iso': '256.a', 'p': 11, 'prec': 20, 'unit': 48815403749843532056, 'val': 1}
  • id: 2412
    {'lmfdb_iso': '256.a', 'p': 17, 'prec': 20, 'unit': 71727371340472865497265, 'val': 1}
  • id: 2413
    {'lmfdb_iso': '256.a', 'p': 19, 'prec': 20, 'unit': 643004995408580721966808, 'val': 1}
  • id: 2410
    {'lmfdb_iso': '256.a', 'p': 41, 'prec': 20, 'unit': 1931124926570823835489623546032, 'val': 1}
  • id: 2414
    {'lmfdb_iso': '256.a', 'p': 43, 'prec': 20, 'unit': 2186833488071702738969187293862, 'val': 1}
  • id: 2417
    {'lmfdb_iso': '256.a', 'p': 59, 'prec': 20, 'unit': 2426319747471867108906270119515623, 'val': 1}
  • id: 2409
    {'lmfdb_iso': '256.a', 'p': 67, 'prec': 20, 'unit': 27560147851288211011174015435009243, 'val': 1}
  • id: 2415
    {'lmfdb_iso': '256.a', 'p': 73, 'prec': 20, 'unit': 115321793534711387853396449477648896, 'val': 1}
  • id: 2408
    {'lmfdb_iso': '256.a', 'p': 83, 'prec': 20, 'unit': 2650733885986241046376208746861402806, 'val': 1}
  • id: 2416
    {'lmfdb_iso': '256.a', 'p': 89, 'prec': 20, 'unit': 966113717534111062418643745797891591, 'val': 1}
  • id: 2407
    {'lmfdb_iso': '256.a', 'p': 97, 'prec': 20, 'unit': 34173650191880997027790988986633483337, 'val': 1}