Elliptic curve data - 51744.r1

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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': '51744p', 'Clabel': '51744p1', 'Cnumber': 1, 'abc_quality': 1.1423859289548068, 'absD': 338116062581232832512, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 132, 'ainvs': [0, -1, 0, -743633, -918227967], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 51744, 'degree': 1128960, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6222029416313625550523586809', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1], 'jinv': [-226591821421000000, 1684650343696353], 'lmfdb_iso': '51744.r', 'lmfdb_label': '51744.r1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -743633, -918227967], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['132.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.5631973225699977071042699933', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1617], [3, 4, 17248], [5, 2, 4704], [7, 14, 352], [11, 12, 4704]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6047374028955316947842344355', 'prec': 100}, 'szpiro_ratio': 5.048763215756701, '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, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -3, 0, -3, 0], 'aplist': [0, -1, 0, 0, 1, 0, -3, -3, -3, 3, 6, 5, -2, 7, 3, -12, -5, 2, 4, -13, 8, -8, -4, 8, 9], 'class_deg': 1, 'class_size': 1, 'conductor': 51744, 'isogeny_matrix': [[1]], 'lmfdb_iso': '51744.r', 'trace_hash': 877089440981679410}
• 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': '0.0052769558913027107705369594584', 'prec': 110}, 'conductor': 51744, 'gens': [[4144, 259127, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '6.5631973225699977071042699933', 'prec': 100}], 'lmfdb_label': '51744.r1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.071903369572973237806561624578', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7191600266509899373936008704191034595', 'prec': 130}, 'tamagawa_product': 10, 'torsion_generators': [], 'xcoord_integral_points': [4144]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 1, 0], '7': 'a', '11': [2, 0], '13': [1, 3, 0], '17': [3, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '51744.r1'}
• ec_torsion_growth •

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

  
  
  • id: 2505719
    {'degree': 3, 'field': [-6, 12, -1, 1], 'lmfdb_label': '51744.r1', 'torsion': [2]}
  • id: 2505720
    {'degree': 6, 'field': [2673, 0, 31, 0, -17, 0, 1], 'lmfdb_label': '51744.r1', 'torsion': [2, 2]}
  • id: 2505721
    {'degree': 8, 'field': [-147, 0, -1736, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '51744.r1', 'torsion': [3]}
  • id: 2505722
    {'degree': 12, 'field': [936096, 838096, 74872, -174832, -67228, -5488, -1008, 392, 560, -28, -42, 0, 1], 'lmfdb_label': '51744.r1', '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: 1238294
    {'conductor': 51744, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '51744.r1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1238295
    {'conductor': 51744, 'conductor_valuation': 1, 'discriminant_valuation': 21, 'j_denominator_valuation': 21, 'kodaira_symbol': 25, 'lmfdb_label': '51744.r1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1238296
    {'conductor': 51744, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '51744.r1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1238297
    {'conductor': 51744, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '51744.r1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
• 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': [[89, 2, 89, 3], [1, 2, 0, 1], [67, 2, 67, 3], [1, 0, 2, 1], [131, 2, 130, 3], [13, 2, 13, 3], [1, 1, 131, 0]], 'adelic_image': '132.2.0.?', 'conductor': 51744, 'lmfdb_label': '51744.r1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2603934
    {'lmfdb_iso': '51744.r', 'p': 17, 'prec': 20, 'unit': 1219687767678719496282, 'val': 2}
  • id: 2603925
    {'lmfdb_iso': '51744.r', 'p': 19, 'prec': 20, 'unit': 736424355636436006414519, 'val': 1}
  • id: 2603939
    {'lmfdb_iso': '51744.r', 'p': 23, 'prec': 20, 'unit': 29173606203366823983298144, 'val': 1}
  • id: 2603932
    {'lmfdb_iso': '51744.r', 'p': 29, 'prec': 20, 'unit': 885243833952621726123259005, 'val': 1}
  • id: 2603943
    {'lmfdb_iso': '51744.r', 'p': 31, 'prec': 20, 'unit': 18231430792228883509740047027, 'val': 1}
  • id: 2603928
    {'lmfdb_iso': '51744.r', 'p': 37, 'prec': 20, 'unit': 232027484119635530525494294090, 'val': 1}
  • id: 2603930
    {'lmfdb_iso': '51744.r', 'p': 41, 'prec': 20, 'unit': 383423867643350188014340439951, 'val': 1}
  • id: 2603931
    {'lmfdb_iso': '51744.r', 'p': 43, 'prec': 20, 'unit': 5199766181960846561089040526918, 'val': 1}
  • id: 2603941
    {'lmfdb_iso': '51744.r', 'p': 47, 'prec': 20, 'unit': 36239515554589930558067369797452, 'val': 1}
  • id: 2603936
    {'lmfdb_iso': '51744.r', 'p': 53, 'prec': 20, 'unit': 187415838169603363323119919008149, 'val': 1}
  • id: 2603937
    {'lmfdb_iso': '51744.r', 'p': 59, 'prec': 20, 'unit': 3430173208105605914188667814818037, 'val': 1}
  • id: 2603942
    {'lmfdb_iso': '51744.r', 'p': 61, 'prec': 20, 'unit': 1511023200464548722456239897490591, 'val': 1}
  • id: 2603927
    {'lmfdb_iso': '51744.r', 'p': 67, 'prec': 20, 'unit': 38984400420786632375895261105113351, 'val': 1}
  • id: 2603929
    {'lmfdb_iso': '51744.r', 'p': 71, 'prec': 20, 'unit': 141540541687863187696590614640009423, 'val': 1}
  • id: 2603938
    {'lmfdb_iso': '51744.r', 'p': 73, 'prec': 20, 'unit': 88481585757704258131615130063742128, 'val': 1}
  • id: 2603933
    {'lmfdb_iso': '51744.r', 'p': 79, 'prec': 20, 'unit': 510542065401073708602345045717720698, 'val': 1}
  • id: 2603935
    {'lmfdb_iso': '51744.r', 'p': 83, 'prec': 20, 'unit': 171992783402307972132461131484540642, 'val': 1}
  • id: 2603940
    {'lmfdb_iso': '51744.r', 'p': 89, 'prec': 20, 'unit': 8493729197293780490773930199122931148, 'val': 1}
  • id: 2603926
    {'lmfdb_iso': '51744.r', 'p': 97, 'prec': 20, 'unit': 40094397874384240679170508213411847950, 'val': 1}