Elliptic curve data - 31814.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': '31814a', 'Clabel': '31814a1', 'Cnumber': 1, 'abc_quality': 0.7262290590930661, 'absD': 63628, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 31814, 'ainvs': [1, 0, 1, 2, 12], 'analytic_rank': 3, 'bad_primes': [2, 15907], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 31814, 'degree': 5808, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.39838047800450585805893483546', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [1685159, 63628], 'lmfdb_iso': '31814.a', 'lmfdb_label': '31814.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 2, 12], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['31814.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 30, 'optimality': 1, 'potential_good_reduction': False, 'rank': 3, 'regulator': {'__RealLiteral__': 0, 'data': '0.88306019809114896025352746205', 'prec': 103}, 'semistable': True, 'serre_invariants': [[2, 4, 15907], [15907, 15908, 2]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.39838047800450585805893483546', 'prec': 107}, 'szpiro_ratio': 1.7844026908976405, '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, -1, -2, 1, -4, 2, -4, -1, 1, 4, -2, -2, -4, 4, 8, 1, 0, -1, -4, -4], 'aplist': [-1, -2, -4, -4, -2, -4, 0, -4, -5, -8, -4, -5, -9, -10, -6, -3, 4, -13, -3, -12, -4, 3, 0, 4, -1], 'class_deg': 1, 'class_size': 1, 'conductor': 31814, 'isogeny_matrix': [[1]], 'lmfdb_iso': '31814.a', 'trace_hash': 2129322592080999877}
• 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': '2.2183439654534653331450820805', 'prec': 100}, 'conductor': 31814, 'gens': [[-1, 3, 1], [1, 3, 1], [3, 5, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.93845849979430434804516971670', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.0178533338050135956553668334', 'prec': 100}, {'__RealLiteral__': 0, 'data': '1.2955692484043719114722399831', 'prec': 100}], 'lmfdb_label': '31814.a1', 'ngens': 3, 'rank_bounds': [3, 3], 'real_period': {'__RealLiteral__': 0, 'data': '2.6415376732824197906735278245', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999997', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6652735620680126853229974528124478388', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [-2, -1, 0, 1, 3, 4, 9, 12, 15, 26, 43, 55, 186, 265, 531]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [3, 0], '5': [7, 0], '7': [3, 0], '11': [3, 0], '13': [3, 0], '17': [3, 3, 0], '19': [3, 0], '23': [3, 0], '29': [3, 0], '31': [3, 0], '37': [3, 0], '41': [5, 0], '43': [3, 0], '47': [3, 0], '15907': 'o?'}, 'iwp0': 0, 'lmfdb_label': '31814.a1'}
• ec_torsion_growth •

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

  
  
  • id: 1584778
    {'degree': 3, 'field': [-21, 10, 0, 1], 'lmfdb_label': '31814.a1', 'torsion': [2]}
  • id: 1584779
    {'degree': 6, 'field': [15907, 0, 900, 0, 60, 0, 1], 'lmfdb_label': '31814.a1', 'torsion': [2, 2]}
  • id: 1584780
    {'degree': 8, 'field': [162, -1323, 1368, -91, 49, -7, 7, -4, 1], 'lmfdb_label': '31814.a1', 'torsion': [3]}
  • id: 1584781
    {'degree': 12, 'field': [7970176, -1584896, 5242464, -4016176, 318582, 404802, -84793, -13128, 3601, 346, -79, -4, 1], 'lmfdb_label': '31814.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: 742886
    {'conductor': 31814, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '31814.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 742887
    {'conductor': 31814, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '31814.a1', 'prime': 15907, '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': [[1, 1, 31813, 0], [15909, 2, 15909, 3], [1, 0, 2, 1], [1, 2, 0, 1], [31813, 2, 31812, 3]], 'adelic_image': '31814.2.0.?', 'conductor': 31814, 'lmfdb_label': '31814.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 1547705
    {'lmfdb_iso': '31814.a', 'p': 5, 'prec': 20, 'unit': 5255538763, 'val': 2}
  • id: 1547706
    {'lmfdb_iso': '31814.a', 'p': 7, 'prec': 20, 'unit': 194209107351117, 'val': 3}
  • id: 1547704
    {'lmfdb_iso': '31814.a', 'p': 11, 'prec': 20, 'unit': 921678657644433886, 'val': 3}
  • id: 1547711
    {'lmfdb_iso': '31814.a', 'p': 13, 'prec': 20, 'unit': 209342824187052272720, 'val': 3}
  • id: 1547714
    {'lmfdb_iso': '31814.a', 'p': 19, 'prec': 20, 'unit': 349015064584785198084695, 'val': 3}
  • id: 1547717
    {'lmfdb_iso': '31814.a', 'p': 23, 'prec': 20, 'unit': 25501460066959693005042848, 'val': 3}
  • id: 1547710
    {'lmfdb_iso': '31814.a', 'p': 29, 'prec': 20, 'unit': 439834751740694471749822214, 'val': 3}
  • id: 1547707
    {'lmfdb_iso': '31814.a', 'p': 31, 'prec': 20, 'unit': 13707325064172912602299759381, 'val': 3}
  • id: 1547722
    {'lmfdb_iso': '31814.a', 'p': 37, 'prec': 20, 'unit': 10634175169328533284874207619, 'val': 3}
  • id: 1547708
    {'lmfdb_iso': '31814.a', 'p': 41, 'prec': 20, 'unit': 65397518225949949146007966674, 'val': 4}
  • id: 1547709
    {'lmfdb_iso': '31814.a', 'p': 43, 'prec': 20, 'unit': 984531797755587698662394349925, 'val': 3}
  • id: 1547720
    {'lmfdb_iso': '31814.a', 'p': 47, 'prec': 20, 'unit': 10587929421968396502814466016433, 'val': 3}
  • id: 1547715
    {'lmfdb_iso': '31814.a', 'p': 53, 'prec': 20, 'unit': 137122717233388352738870106276329, 'val': 3}
  • id: 1547713
    {'lmfdb_iso': '31814.a', 'p': 59, 'prec': 20, 'unit': 2358280082773340493349722679041158, 'val': 3}
  • id: 1547721
    {'lmfdb_iso': '31814.a', 'p': 61, 'prec': 20, 'unit': 3275653424468749398978256604771983, 'val': 3}
  • id: 1547703
    {'lmfdb_iso': '31814.a', 'p': 67, 'prec': 20, 'unit': 33938303495745895112830349418036718, 'val': 3}
  • id: 1547719
    {'lmfdb_iso': '31814.a', 'p': 71, 'prec': 20, 'unit': 130926825521090046446869158548481945, 'val': 3}
  • id: 1547716
    {'lmfdb_iso': '31814.a', 'p': 73, 'prec': 20, 'unit': 196204832411161859346758068678894941, 'val': 3}
  • id: 1547712
    {'lmfdb_iso': '31814.a', 'p': 79, 'prec': 20, 'unit': 60341382220174582882013650577265002, 'val': 3}
  • id: 1547718
    {'lmfdb_iso': '31814.a', 'p': 89, 'prec': 20, 'unit': 3860046634362991946782518502543972316, 'val': 3}
  • id: 1547702
    {'lmfdb_iso': '31814.a', 'p': 97, 'prec': 20, 'unit': 31640772072228041259486072032474027426, 'val': 3}