Elliptic curve data - 14112.b1

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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': '14112bc', 'Clabel': '14112bc2', 'Cnumber': 2, 'abc_quality': 1.0347941470054765, 'absD': 7115122531830362112, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 84, 'ainvs': [0, 0, 0, -663852, -163926560], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 14112, 'degree': 368640, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3309161147141925024673303683', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [92100460096, 20253807], 'lmfdb_iso': '14112.b', 'lmfdb_label': '14112.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1505, -17199], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '28.6.0.a.1', '84.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.3358401462656047818794782355', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 441], [3, 8, 1568], [7, 32, 288]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.11550771529253569479979925666', 'prec': 103}, 'szpiro_ratio': 5.424619127512857, '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, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -4, 0], 'aplist': [0, 0, -4, 0, -2, 2, 0, -4, -6, 10, -8, 10, -4, 8, 4, -10, -8, 6, -4, 14, -6, -4, 12, 4, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 14112, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '14112.b', 'trace_hash': 1292410597035311156}
• 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': '0.0094491335507783684752475991784', 'prec': 110}, 'conductor': 14112, 'gens': [[-574, 5292, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3358401462656047818794782355', 'prec': 100}], 'lmfdb_label': '14112.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16987682267393950421863097693', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1744408185746484668952408140015452835', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-280, 0, 1]], 'xcoord_integral_points': [-574, -280, 1178]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': 'a', '11': [3, 0], '13': [1, 0], '17': [1, 1, 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': '14112.b1'}
• ec_torsion_growth •

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

  
  
  • id: 725435
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '14112.b1', 'torsion': [2, 2]}
  • id: 725436
    {'degree': 4, 'field': [7, 0, -5, 0, 1], 'lmfdb_label': '14112.b1', 'torsion': [4]}
  • id: 725439
    {'degree': 8, 'field': [-894, 3092, -3776, 2028, -544, 52, 18, -4, 1], 'lmfdb_label': '14112.b1', 'torsion': [6]}
  • id: 725437
    {'degree': 8, 'field': [9, -24, 202, 72, -160, 20, -2, -4, 1], 'lmfdb_label': '14112.b1', 'torsion': [2, 4]}
  • id: 725438
    {'degree': 8, 'field': [81, -54, 36, 36, -21, 12, 4, -2, 1], 'lmfdb_label': '14112.b1', 'torsion': [2, 4]}
  • id: 725441
    {'degree': 16, 'field': [-342, 780, 1212, -2004, -3024, 2472, 2454, -1588, -961, 700, -30, 44, -68, 0, 20, -8, 1], 'lmfdb_label': '14112.b1', 'torsion': [2, 6]}
  • id: 725440
    {'degree': 16, 'field': [423801, 0, 516852, 0, 215124, 0, 24108, 0, -5234, 0, -1396, 0, 36, 0, 20, 0, 1], 'lmfdb_label': '14112.b1', 'torsion': [8]}
• 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: 309259
    {'conductor': 14112, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '14112.b1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 309260
    {'conductor': 14112, 'conductor_valuation': 2, 'discriminant_valuation': 16, 'j_denominator_valuation': 10, 'kodaira_symbol': -14, 'lmfdb_label': '14112.b1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 309261
    {'conductor': 14112, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '14112.b1', 'prime': 7, 'reduction_type': 0, '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: 1757745
    {'adelic_gens': [[64, 25, 21, 64], [62, 1, 11, 0], [1, 4, 0, 1], [29, 4, 58, 9], [1, 0, 4, 1], [81, 4, 80, 5], [3, 4, 8, 11], [1, 2, 2, 5]], 'adelic_image': '84.12.0.?', 'conductor': 14112, 'lmfdb_label': '14112.b1', 'prime': 0}
  • id: 66716
    {'conductor': 14112, 'elladic_image': '2.3.0.1', 'lmfdb_label': '14112.b1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 628707
    {'lmfdb_iso': '14112.b', 'p': 5, 'prec': 20, 'unit': 90424970566507, 'val': -1}
  • id: 628706
    {'lmfdb_iso': '14112.b', 'p': 11, 'prec': 20, 'unit': 699571168409241918, 'val': 2}
  • id: 628713
    {'lmfdb_iso': '14112.b', 'p': 13, 'prec': 20, 'unit': 1207175522610761519767, 'val': 1}
  • id: 628716
    {'lmfdb_iso': '14112.b', 'p': 19, 'prec': 20, 'unit': 1294973450006044592393174, 'val': 1}
  • id: 628719
    {'lmfdb_iso': '14112.b', 'p': 23, 'prec': 20, 'unit': 5073189000532865294930099, 'val': 1}
  • id: 628712
    {'lmfdb_iso': '14112.b', 'p': 29, 'prec': 20, 'unit': 2463947957233160028171618292, 'val': 1}
  • id: 628709
    {'lmfdb_iso': '14112.b', 'p': 31, 'prec': 20, 'unit': 13776191491220175239636105706, 'val': 1}
  • id: 628724
    {'lmfdb_iso': '14112.b', 'p': 37, 'prec': 20, 'unit': 228016826210824887394683661711, 'val': 1}
  • id: 628710
    {'lmfdb_iso': '14112.b', 'p': 41, 'prec': 20, 'unit': 2270037721597099369990281314174, 'val': 1}
  • id: 628711
    {'lmfdb_iso': '14112.b', 'p': 43, 'prec': 20, 'unit': 2765640465991385399497019992272, 'val': 1}
  • id: 628721
    {'lmfdb_iso': '14112.b', 'p': 47, 'prec': 20, 'unit': 47928171641089563065815711821810, 'val': 1}
  • id: 628717
    {'lmfdb_iso': '14112.b', 'p': 53, 'prec': 20, 'unit': 159607555464482741236291195528021, 'val': 1}
  • id: 628715
    {'lmfdb_iso': '14112.b', 'p': 59, 'prec': 20, 'unit': 3796849227115618787237488521932391, 'val': 1}
  • id: 628722
    {'lmfdb_iso': '14112.b', 'p': 61, 'prec': 20, 'unit': 7899501961144542138029028005580781, 'val': 1}
  • id: 628705
    {'lmfdb_iso': '14112.b', 'p': 67, 'prec': 20, 'unit': 37659591315012259900669107218281410, 'val': 1}
  • id: 628708
    {'lmfdb_iso': '14112.b', 'p': 71, 'prec': 20, 'unit': 41085567119553563366497021801093249, 'val': 1}
  • id: 628718
    {'lmfdb_iso': '14112.b', 'p': 73, 'prec': 20, 'unit': 177187426836789705864548293803180586, 'val': 1}
  • id: 628714
    {'lmfdb_iso': '14112.b', 'p': 79, 'prec': 20, 'unit': 341513984707963236787786915980111758, 'val': 1}
  • id: 628723
    {'lmfdb_iso': '14112.b', 'p': 83, 'prec': 20, 'unit': 1176710849676649347420908974956789791, 'val': 1}
  • id: 628720
    {'lmfdb_iso': '14112.b', 'p': 89, 'prec': 20, 'unit': 4503051561708788213606224735111443810, 'val': 1}
  • id: 628704
    {'lmfdb_iso': '14112.b', 'p': 97, 'prec': 20, 'unit': 43179125798467496094759101935015246098, 'val': 1}