Elliptic curve data - 57.a1

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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': '57a', 'Clabel': '57a1', 'Cnumber': 1, 'abc_quality': 0.8651174046959357, 'absD': 171, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 38, 'ainvs': [0, -1, 1, -2, 2], 'analytic_rank': 1, 'bad_primes': [3, 19], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 57, 'degree': 4, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.83654840927857264432908623559', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [-1404928, 171], 'lmfdb_iso': '57.a', 'lmfdb_label': '57.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -2, 2], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['38.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 12, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.037574592736823752824805111217', 'prec': 107}, 'semistable': True, 'serre_invariants': [[2, 2, 19], [3, 4, 19], [19, 20, 3]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.83654840927857264432908623559', 'prec': 107}, 'szpiro_ratio': 3.548405037331394, '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, -2, -1, 2, -3, 2, -5, 0, 1, 6, 1, -2, 2, 10, 3, -4, -1, -2, -1, -6], 'aplist': [-2, -1, -3, -5, 1, 2, -1, -1, -4, -2, -6, 0, 0, -1, -9, 10, -8, -1, 8, -12, -11, 16, 12, -6, -10], 'class_deg': 1, 'class_size': 1, 'conductor': 57, 'isogeny_matrix': [[1]], 'lmfdb_iso': '57.a', 'trace_hash': 1883722513434514463}
• 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': '5.3286441159112314993311429764', 'prec': 100}, 'conductor': 57, 'gens': [[2, 1, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.037574592736823752824805111217', 'prec': 107}], 'lmfdb_label': '57.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '5.5555045213725043221174270349', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999999', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '0.41749163967630964038932049159583966692', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [-1, 0, 1, 2, 4, 11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 4, 0], '3': [1, 0], '5': [5, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '57.a1'}
• ec_torsion_growth •

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

  
  
  • id: 2004
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '57.a1', 'torsion': [2]}
  • id: 2005
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '57.a1', 'torsion': [2, 2]}
  • id: 2006
    {'degree': 8, 'field': [-13, 25, -34, 17, -5, -7, 7, -4, 1], 'lmfdb_label': '57.a1', 'torsion': [3]}
  • id: 2007
    {'degree': 12, 'field': [-13, 18, -38, 20, -31, 12, -16, 4, -11, -6, 10, -4, 1], 'lmfdb_label': '57.a1', '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: 288
    {'conductor': 57, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '57.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 289
    {'conductor': 57, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57.a1', '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

  
  {'adelic_gens': [[37, 2, 36, 3], [1, 2, 0, 1], [1, 0, 2, 1], [21, 2, 21, 3], [1, 1, 37, 0]], 'adelic_image': '38.2.0.?', 'conductor': 57, 'lmfdb_label': '57.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 23
    {'lmfdb_iso': '57.a', 'p': 5, 'prec': 20, 'unit': 1976753374646, 'val': 2}
  • id: 24
    {'lmfdb_iso': '57.a', 'p': 7, 'prec': 20, 'unit': 768748635208678, 'val': 1}
  • id: 22
    {'lmfdb_iso': '57.a', 'p': 11, 'prec': 20, 'unit': 499492802849643986506, 'val': -1}
  • id: 28
    {'lmfdb_iso': '57.a', 'p': 13, 'prec': 20, 'unit': 207595350535820685029, 'val': 1}
  • id: 30
    {'lmfdb_iso': '57.a', 'p': 17, 'prec': 20, 'unit': 130946564692834016524382, 'val': 1}
  • id: 34
    {'lmfdb_iso': '57.a', 'p': 23, 'prec': 20, 'unit': 56081759290944559769151873, 'val': 1}
  • id: 27
    {'lmfdb_iso': '57.a', 'p': 29, 'prec': 20, 'unit': 1466584299367632254290479342, 'val': 1}
  • id: 39
    {'lmfdb_iso': '57.a', 'p': 31, 'prec': 20, 'unit': 8033117094336313365862228119, 'val': 1}
  • id: 26
    {'lmfdb_iso': '57.a', 'p': 43, 'prec': 20, 'unit': 815002683752035324571290805930, 'val': 1}
  • id: 37
    {'lmfdb_iso': '57.a', 'p': 47, 'prec': 20, 'unit': 26572787247710859265325835486036, 'val': 1}
  • id: 32
    {'lmfdb_iso': '57.a', 'p': 53, 'prec': 20, 'unit': 45852129346987477088171716762808, 'val': 1}
  • id: 33
    {'lmfdb_iso': '57.a', 'p': 59, 'prec': 20, 'unit': 2137166989452179241986499404474612, 'val': 1}
  • id: 38
    {'lmfdb_iso': '57.a', 'p': 61, 'prec': 20, 'unit': 580831370079961787683331532578228, 'val': 1}
  • id: 31
    {'lmfdb_iso': '57.a', 'p': 67, 'prec': 20, 'unit': 7796357392536620939497757119082449, 'val': 1}
  • id: 36
    {'lmfdb_iso': '57.a', 'p': 71, 'prec': 20, 'unit': 27702461839017253823264826072674518, 'val': 1}
  • id: 25
    {'lmfdb_iso': '57.a', 'p': 73, 'prec': 20, 'unit': 205247246042351333288340930225357860, 'val': 1}
  • id: 29
    {'lmfdb_iso': '57.a', 'p': 79, 'prec': 20, 'unit': 845723348997509437956448579824600410, 'val': 1}
  • id: 21
    {'lmfdb_iso': '57.a', 'p': 83, 'prec': 20, 'unit': 1505057413303891837309517348301860679, 'val': 1}
  • id: 35
    {'lmfdb_iso': '57.a', 'p': 89, 'prec': 20, 'unit': 7694313128331925897355284425637787655, 'val': 1}
  • id: 20
    {'lmfdb_iso': '57.a', 'p': 97, 'prec': 20, 'unit': 24183177915756278105614547381441047859, 'val': 1}