Elliptic curve data - 51714.t2

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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': '51714v', 'Clabel': '51714v2', 'Cnumber': 2, 'abc_quality': 1.0059757193751666, 'absD': 72841500317455117762176, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1768, 'ainvs': [1, -1, 1, 9964039, 4694204441], 'analytic_rank': 0, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 51714, 'degree': 4816896, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0756407892198912654525115850', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2], 'jinv': [31091549545392623, 20700995942016], 'lmfdb_iso': '51714.t', 'lmfdb_label': '51714.t2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 6551, -78631], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '68.6.0.c.1', '104.6.0.?', '1768.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2438599661550680517281452458', 'prec': 100}, 'szpiro_ratio': 5.524224603525925, '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, 0, 1, -2, 0, 4, 1, 0, -2, -2, 0, 0, 4, 0, 1, 1, 0, 0, -2], 'aplist': [1, 0, -2, 4, -2, 0, 1, 0, 2, 0, 8, 2, -8, -4, 0, -2, -4, 8, 8, 0, -4, -6, 16, 14, -4], 'class_deg': 2, 'class_size': 2, 'conductor': 51714, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '51714.t', 'trace_hash': 1972894270519838705}
• 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': '0.0021307492971127476209627840007', 'prec': 110}, 'conductor': 51714, 'gens': [], 'heights': [], 'lmfdb_label': '51714.t2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.068570467462751426947401799982', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8399461779140799090545007989852190440', 'prec': 130}, 'tamagawa_product': 224, 'torsion_generators': [[-1845, 1841, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 1], '3': 'a', '5': [0, 0], '7': [2, 0], '13': 'a', '17': [1, 0]}, 'iwp0': 11, 'lmfdb_label': '51714.t2'}
• ec_torsion_growth •

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

  
  
  • id: 2504808
    {'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '51714.t2', 'torsion': [2, 2]}
  • id: 2504809
    {'degree': 4, 'field': [-936, 0, 9, 0, 1], 'lmfdb_label': '51714.t2', 'torsion': [4]}
  • id: 2504812
    {'degree': 8, 'field': [-764, -412, 310, 203, -98, -7, 7, -4, 1], 'lmfdb_label': '51714.t2', 'torsion': [6]}
  • id: 2504811
    {'degree': 8, 'field': [67882, -17420, 24706, 10960, 891, 152, 58, -4, 1], 'lmfdb_label': '51714.t2', 'torsion': [2, 4]}
  • id: 2504810
    {'degree': 8, 'field': [456976, 0, 70304, 0, 4290, 0, 104, 0, 1], 'lmfdb_label': '51714.t2', 'torsion': [2, 4]}
  • id: 2504813
    {'degree': 16, 'field': [116985856, 0, 38069897216, 0, -5512304512, 0, 296397504, 0, -5320696, 0, -234696, 0, 13385, 0, -184, 0, 1], 'lmfdb_label': '51714.t2', 'torsion': [8]}
  • id: 2504814
    {'degree': 16, 'field': [1396965376, 0, 986644480, 0, 87829504, 0, -3665504, 0, -1363040, 0, 21928, 0, 1732, 0, 52, 0, 1], 'lmfdb_label': '51714.t2', '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: 1237796
    {'conductor': 51714, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '51714.t2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 1237797
    {'conductor': 51714, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '51714.t2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1237798
    {'conductor': 51714, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '51714.t2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1237799
    {'conductor': 51714, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '51714.t2', '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: 2007711
    {'adelic_gens': [[1226, 1, 271, 0], [1, 2, 2, 5], [1548, 225, 1105, 664], [1, 4, 0, 1], [1765, 4, 1764, 5], [2, 1, 883, 0], [1, 0, 4, 1], [3, 4, 8, 11], [105, 4, 210, 9]], 'adelic_image': '1768.12.0.?', 'conductor': 51714, 'lmfdb_label': '51714.t2', 'prime': 0}
  • id: 221308
    {'conductor': 51714, 'elladic_image': '2.3.0.1', 'lmfdb_label': '51714.t2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 51714.t does not appear in ec_padic