Elliptic curve data - 31200.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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '31200bq', 'Clabel': '31200bq3', 'Cnumber': 3, 'abc_quality': 0.9081603122524584, 'absD': 10281960000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 520, 'ainvs': [0, -1, 0, -13408, 581812], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 31200, 'degree': 73728, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2644656268961680252433980885', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [33324076232, 1285245], 'lmfdb_iso': '31200.a', 'lmfdb_label': '31200.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -536, -4440], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '40.24.0-40.v.1.3', '104.24.0.?', '520.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 11, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3533013658469342342091192572', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.060113714740841144119905669206', 'prec': 110}, 'szpiro_ratio': 3.877447413463291, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, -4, 0, 1, 0, 4, 0, 1, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, -1, 0, -4, 4, 1, -2, -4, 0, 6, 0, -10, 2, 4, -4, 6, -4, -2, 4, -8, 2, 16, -4, 10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 31200, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '31200.a', 'trace_hash': 1340698022588971734}
• 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': '0.079744201071947911219396253662', 'prec': 107}, 'conductor': 31200, 'gens': [[52, 150, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3533013658469342342091192572', 'prec': 100}], 'lmfdb_label': '31200.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.71725366599731205108378246481', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8826414634115326776309976834856785681', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[12, 650, 1]], 'xcoord_integral_points': [-92, 12, 52, 77, 221, 337]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': [1, 0], '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [3, 0]}, 'iwp0': 0, 'lmfdb_label': '31200.a2'}
• ec_torsion_growth •

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

  
  
  • id: 1556067
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '31200.a2', 'torsion': [2, 4]}
  • id: 1556068
    {'degree': 4, 'field': [360, 0, -20, 0, 1], 'lmfdb_label': '31200.a2', 'torsion': [8]}
  • id: 1556071
    {'degree': 8, 'field': [-17924, -34800, -16488, 3360, 2768, -120, -108, 0, 1], 'lmfdb_label': '31200.a2', 'torsion': [2, 8]}
  • id: 1556069
    {'degree': 8, 'field': [8281, 0, -1076, 0, 186, 0, 4, 0, 1], 'lmfdb_label': '31200.a2', 'torsion': [4, 4]}
  • id: 1556070
    {'degree': 8, 'field': [26536, 36960, 17936, 3360, 116, -120, -4, 0, 1], 'lmfdb_label': '31200.a2', 'torsion': [2, 8]}
  • id: 1556072
    {'degree': 8, 'field': [28945, 920, -7124, 476, 610, -40, -20, -4, 1], 'lmfdb_label': '31200.a2', 'torsion': [12]}
  • id: 1556074
    {'degree': 16, 'field': [2640625, 0, -2112500, 0, 422500, 0, -262500, 0, 62250, 0, 300, 0, 100, 0, -20, 0, 1], 'lmfdb_label': '31200.a2', 'torsion': [2, 12]}
  • id: 1556073
    {'degree': 16, 'field': [443523600, 0, -197121600, 0, 26114400, 0, -842400, 0, 171720, 0, -23760, 0, 1640, 0, -40, 0, 1], 'lmfdb_label': '31200.a2', 'torsion': [16]}
• 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: 728022
    {'conductor': 31200, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '31200.a2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 728023
    {'conductor': 31200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '31200.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 728024
    {'conductor': 31200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '31200.a2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 728025
    {'conductor': 31200, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '31200.a2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1872405
    {'adelic_gens': [[41, 8, 164, 33], [513, 8, 512, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [329, 328, 78, 335], [328, 73, 187, 174], [304, 517, 515, 518], [7, 6, 514, 515]], 'adelic_image': '520.48.0.?', 'conductor': 31200, 'lmfdb_label': '31200.a2', 'prime': 0}
  • id: 139706
    {'conductor': 31200, 'elladic_image': '4.12.0.7', 'lmfdb_label': '31200.a2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1514519
    {'lmfdb_iso': '31200.a', 'p': 7, 'prec': 20, 'unit': 6453194479971730, 'val': 1}
  • id: 1514524
    {'lmfdb_iso': '31200.a', 'p': 11, 'prec': 20, 'unit': 30835779363233988078, 'val': 1}
  • id: 1514525
    {'lmfdb_iso': '31200.a', 'p': 17, 'prec': 20, 'unit': 119647627637956489345969, 'val': 1}
  • id: 1514526
    {'lmfdb_iso': '31200.a', 'p': 19, 'prec': 20, 'unit': 1451815262161627605424070, 'val': 1}
  • id: 1514522
    {'lmfdb_iso': '31200.a', 'p': 29, 'prec': 20, 'unit': 313335065343532364757523470, 'val': 1}
  • id: 1514518
    {'lmfdb_iso': '31200.a', 'p': 37, 'prec': 20, 'unit': 252599773187050690837719973656, 'val': 1}
  • id: 1514520
    {'lmfdb_iso': '31200.a', 'p': 41, 'prec': 20, 'unit': 144604123457078020461915343442, 'val': 1}
  • id: 1514521
    {'lmfdb_iso': '31200.a', 'p': 43, 'prec': 20, 'unit': 1295604716673884733615462825272, 'val': 1}
  • id: 1514532
    {'lmfdb_iso': '31200.a', 'p': 47, 'prec': 20, 'unit': 318411940739215036684686610602, 'val': 2}
  • id: 1514527
    {'lmfdb_iso': '31200.a', 'p': 53, 'prec': 20, 'unit': 233254519320673223899875672262336, 'val': 1}
  • id: 1514528
    {'lmfdb_iso': '31200.a', 'p': 59, 'prec': 20, 'unit': 1310036925067858636685989255916006, 'val': 1}
  • id: 1514533
    {'lmfdb_iso': '31200.a', 'p': 61, 'prec': 20, 'unit': 4891245596760609869060440917710403, 'val': 1}
  • id: 1514517
    {'lmfdb_iso': '31200.a', 'p': 67, 'prec': 20, 'unit': 35432523720600036792114861852280779, 'val': 1}
  • id: 1514531
    {'lmfdb_iso': '31200.a', 'p': 71, 'prec': 20, 'unit': 32499651277333688239652229209843776, 'val': 1}
  • id: 1514529
    {'lmfdb_iso': '31200.a', 'p': 73, 'prec': 20, 'unit': 222975294098213784660968729126853514, 'val': 1}
  • id: 1514523
    {'lmfdb_iso': '31200.a', 'p': 79, 'prec': 20, 'unit': 248302387716727254706719731755220202, 'val': 1}
  • id: 1514516
    {'lmfdb_iso': '31200.a', 'p': 83, 'prec': 20, 'unit': 2869759712668061205142372708219300314, 'val': 1}
  • id: 1514530
    {'lmfdb_iso': '31200.a', 'p': 89, 'prec': 20, 'unit': 9790871614179036905238184253796415561, 'val': 1}
  • id: 1514515
    {'lmfdb_iso': '31200.a', 'p': 97, 'prec': 20, 'unit': 8678124029636583993097208258119799973, 'val': 1}