Elliptic curve data - 48672.bx1

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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': '48672y', 'Clabel': '48672y1', 'Cnumber': 1, 'abc_quality': 0.9298969596640071, 'absD': 3958108181973504, 'adelic_genus': 1, 'adelic_index': 12, 'adelic_level': 312, 'ainvs': [0, 0, 0, -138411, -20049822], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 48672, 'degree': 314496, 'elladic_images': ['3.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8001793382047152704900448318', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 49, 'isogeny_degrees': [1], 'jinv': [-74088, 1], 'lmfdb_iso': '48672.bx', 'lmfdb_label': '48672.bx1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -91, -338], 'min_quad_twist_disc': 156, 'modell_images': ['3Nn'], 'modm_images': ['3.3.0.a.1', '24.6.0.m.1', '104.2.0.?', '156.6.0.?', '312.12.1.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '34.140315770015292574864826659', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 117], [3, 6, 5408], [13, 62, 288]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1926992096454511093106174589', 'prec': 103}, 'szpiro_ratio': 4.368685475572369, '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, 0, 0, 3, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, -5, 0, -6, 0], 'aplist': [0, 0, 3, 1, 4, 0, -5, -6, 6, 4, 0, -3, -12, -3, 7, 2, -2, -12, -4, -11, 6, -6, 10, -6, 0], 'class_deg': 1, 'class_size': 1, 'conductor': 48672, 'isogeny_matrix': [[1]], 'lmfdb_iso': '48672.bx', 'trace_hash': 851890923370209595}
• 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': '0.027313923830004370723411967643', 'prec': 107}, 'conductor': 48672, 'gens': [[28620893777071102, 4765040348837498252768492, 3636761]], 'heights': [{'__RealLiteral__': 0, 'data': '34.140315770015292574864826659', 'prec': 100}], 'lmfdb_label': '48672.bx1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12365969243450697308323356095', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.4435618954740783608656008002515412178', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [3, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '48672.bx1'}
• ec_torsion_growth •

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

  
  
  • id: 2369910
    {'degree': 3, 'field': [-2, -1, 0, 1], 'lmfdb_label': '48672.bx1', 'torsion': [2]}
  • id: 2369911
    {'degree': 6, 'field': [26, 0, 29, 0, 8, 0, 1], 'lmfdb_label': '48672.bx1', 'torsion': [2, 2]}
  • id: 2369912
    {'degree': 8, 'field': [5266, -3436, -1628, 296, 136, -16, 10, -4, 1], 'lmfdb_label': '48672.bx1', 'torsion': [3]}
  • id: 2369913
    {'degree': 12, 'field': [-91337, -90706, -73188, -23650, -778, 3370, 1286, 178, 92, -102, 8, -6, 1], 'lmfdb_label': '48672.bx1', 'torsion': [4]}
  • id: 2369914
    {'degree': 16, 'field': [4747861, -4059124, -2220264, 4118548, -2017492, 171420, 551950, -563344, 293979, -86920, 17182, -3768, 602, -8, 6, -4, 1], 'lmfdb_label': '48672.bx1', 'torsion': [3, 3]}
• 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: 1163302
    {'conductor': 48672, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48672.bx1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1163303
    {'conductor': 48672, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48672.bx1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1163304
    {'conductor': 48672, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '48672.bx1', 'prime': 13, '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: 1988185
    {'adelic_gens': [[157, 212, 4, 277], [4, 1, 241, 2], [6, 5, 301, 303], [4, 3, 153, 310], [268, 1, 79, 2], [307, 6, 306, 7], [1, 6, 0, 1], [1, 0, 6, 1]], 'adelic_image': '312.12.1.?', 'conductor': 48672, 'lmfdb_label': '48672.bx1', 'prime': 0}
  • id: 209848
    {'conductor': 48672, 'elladic_image': '3.3.0.1', 'lmfdb_label': '48672.bx1', 'modell_image': '3Nn', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2443601
    {'lmfdb_iso': '48672.bx', 'p': 5, 'prec': 20, 'unit': 2587546113591, 'val': 1}
  • id: 2443602
    {'lmfdb_iso': '48672.bx', 'p': 7, 'prec': 20, 'unit': 32629420372509307, 'val': -1}
  • id: 2443607
    {'lmfdb_iso': '48672.bx', 'p': 11, 'prec': 20, 'unit': 9244838548037861298, 'val': 1}
  • id: 2443608
    {'lmfdb_iso': '48672.bx', 'p': 17, 'prec': 20, 'unit': 217650052148490616112878, 'val': 1}
  • id: 2443609
    {'lmfdb_iso': '48672.bx', 'p': 19, 'prec': 20, 'unit': 95961830194762739865229, 'val': 1}
  • id: 2443613
    {'lmfdb_iso': '48672.bx', 'p': 23, 'prec': 20, 'unit': 57243049185747393799001907, 'val': 1}
  • id: 2443605
    {'lmfdb_iso': '48672.bx', 'p': 29, 'prec': 20, 'unit': 4142039753939797054006973756, 'val': 1}
  • id: 2443618
    {'lmfdb_iso': '48672.bx', 'p': 37, 'prec': 20, 'unit': 157314094935691023196245207396, 'val': 1}
  • id: 2443603
    {'lmfdb_iso': '48672.bx', 'p': 41, 'prec': 20, 'unit': 1214335217157294227444493166801, 'val': 1}
  • id: 2443604
    {'lmfdb_iso': '48672.bx', 'p': 43, 'prec': 20, 'unit': 1523140972967003134176550887895, 'val': 1}
  • id: 2443616
    {'lmfdb_iso': '48672.bx', 'p': 47, 'prec': 20, 'unit': 36571501873418454954197323229497, 'val': 1}
  • id: 2443610
    {'lmfdb_iso': '48672.bx', 'p': 53, 'prec': 20, 'unit': 30376963966034026001228964924394, 'val': 1}
  • id: 2443611
    {'lmfdb_iso': '48672.bx', 'p': 59, 'prec': 20, 'unit': 3919497833333810816260157560174515, 'val': 1}
  • id: 2443617
    {'lmfdb_iso': '48672.bx', 'p': 61, 'prec': 20, 'unit': 3025525142090975743707536620758594, 'val': 1}
  • id: 2443600
    {'lmfdb_iso': '48672.bx', 'p': 67, 'prec': 20, 'unit': 28364103548599828681032548586606238, 'val': 1}
  • id: 2443615
    {'lmfdb_iso': '48672.bx', 'p': 71, 'prec': 20, 'unit': 134541160326007423970369361030349564, 'val': 1}
  • id: 2443612
    {'lmfdb_iso': '48672.bx', 'p': 73, 'prec': 20, 'unit': 240775052788897033645554770121521473, 'val': 1}
  • id: 2443606
    {'lmfdb_iso': '48672.bx', 'p': 79, 'prec': 20, 'unit': 1071344992760915960703583015041289347, 'val': 1}
  • id: 2443599
    {'lmfdb_iso': '48672.bx', 'p': 83, 'prec': 20, 'unit': 1967568565531713596410771398371698599, 'val': 1}
  • id: 2443614
    {'lmfdb_iso': '48672.bx', 'p': 89, 'prec': 20, 'unit': 8474812968533001984924388373960252400, 'val': 1}