Elliptic curve data - 1248.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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1248a', 'Clabel': '1248a1', 'Cnumber': 1, 'abc_quality': 0.8784227065314122, 'absD': 67392, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, -1, 0, -14, -12], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1248, 'degree': 128, 'elladic_images': ['4.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.35829830952629706167351690397', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [5088448, 1053], 'lmfdb_iso': '1248.a', 'lmfdb_label': '1248.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -14, -12], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.b.1', '24.12.0-4.b.1.4', '26.6.0.b.1', '52.12.0.e.1', '104.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.83321592084166984275086494661', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.70487189980626971638213296470', 'prec': 107}, 'szpiro_ratio': 2.7494106367805653, '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, -1, 0, -2, 0, -2, 0, 1, 0, 6, 0, -1, 0, 2, 0, -2, 0, 6, 0], 'aplist': [0, -1, -2, -2, 6, -1, -2, 6, 0, -6, -6, 2, -10, -8, -6, 6, 6, -10, -2, 14, -14, -4, -6, 6, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 1248, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1248.a', 'trace_hash': 2281404238021715112}
• 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': '2.0474530765623104517462774170', 'prec': 100}, 'conductor': 1248, 'gens': [[-2, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.83321592084166984275086494661', 'prec': 103}], 'lmfdb_label': '1248.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.4893993991806144313469265703', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0742072127309753004324516863359703391', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-1, 0, 1]], 'xcoord_integral_points': [-2, -1, 8]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1248.a1'}
• ec_torsion_growth •

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

  
  
  • id: 61920
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '1248.a1', 'torsion': [2, 2]}
  • id: 61921
    {'degree': 4, 'field': [5, -2, 0, -2, 1], 'lmfdb_label': '1248.a1', 'torsion': [4]}
  • id: 61924
    {'degree': 8, 'field': [-243, 0, 144, 0, 54, 0, 0, 0, 1], 'lmfdb_label': '1248.a1', 'torsion': [6]}
  • id: 61922
    {'degree': 8, 'field': [9, -6, 2, -10, 7, -6, 8, -4, 1], 'lmfdb_label': '1248.a1', 'torsion': [2, 4]}
  • id: 61923
    {'degree': 8, 'field': [169, 0, -1352, 0, 299, 0, -26, 0, 1], 'lmfdb_label': '1248.a1', 'torsion': [2, 4]}
  • id: 61926
    {'degree': 16, 'field': [169, -1144, -1256, 10200, 34460, 29912, 8760, 7192, 9694, -232, -2520, -8, 260, -120, 40, -8, 1], 'lmfdb_label': '1248.a1', 'torsion': [8]}
  • id: 61925
    {'degree': 16, 'field': [2401, 1372, 4116, 560, 6528, 13732, 13680, 10136, 3154, 668, -132, -224, 72, -28, 24, -8, 1], 'lmfdb_label': '1248.a1', 'torsion': [4, 4]}
  • id: 61927
    {'degree': 16, 'field': [59049, 0, -738720, 0, -536220, 0, -15552, 0, -66, 0, -1952, 0, -204, 0, 0, 0, 1], 'lmfdb_label': '1248.a1', 'torsion': [2, 6]}
• 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: 18479
    {'conductor': 1248, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1248.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 18480
    {'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1248.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 18481
    {'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1248.a1', 'prime': 13, '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

  
  
  • id: 1672410
    {'adelic_gens': [[224, 3, 101, 2], [1, 0, 8, 1], [163, 6, 306, 307], [1, 8, 0, 1], [1, 4, 4, 17], [3, 8, 28, 75], [241, 6, 306, 307], [5, 8, 48, 77], [305, 8, 304, 9], [209, 8, 212, 33]], 'adelic_image': '312.48.0.?', 'conductor': 1248, 'lmfdb_label': '1248.a1', 'prime': 0}
  • id: 5969
    {'conductor': 1248, 'elladic_image': '4.6.0.3', 'lmfdb_label': '1248.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 31130
    {'lmfdb_iso': '1248.a', 'p': 5, 'prec': 20, 'unit': 7491168482887, 'val': 1}
  • id: 31131
    {'lmfdb_iso': '1248.a', 'p': 7, 'prec': 20, 'unit': 10479335382734025, 'val': 1}
  • id: 31137
    {'lmfdb_iso': '1248.a', 'p': 11, 'prec': 20, 'unit': 1143143176526126659, 'val': 1}
  • id: 31138
    {'lmfdb_iso': '1248.a', 'p': 17, 'prec': 20, 'unit': 139073661392143251970828, 'val': 1}
  • id: 31139
    {'lmfdb_iso': '1248.a', 'p': 19, 'prec': 20, 'unit': 443701794193728863485977, 'val': 1}
  • id: 31135
    {'lmfdb_iso': '1248.a', 'p': 29, 'prec': 20, 'unit': 5924624100481590971138206245, 'val': 1}
  • id: 31132
    {'lmfdb_iso': '1248.a', 'p': 31, 'prec': 20, 'unit': 426957615940864663777702910, 'val': 2}
  • id: 31147
    {'lmfdb_iso': '1248.a', 'p': 37, 'prec': 20, 'unit': 562769187663222821198080226061, 'val': 1}
  • id: 31133
    {'lmfdb_iso': '1248.a', 'p': 41, 'prec': 20, 'unit': 3355061775436330679972716414476, 'val': 1}
  • id: 31134
    {'lmfdb_iso': '1248.a', 'p': 43, 'prec': 20, 'unit': 1055849527724031053283820704430, 'val': 1}
  • id: 31145
    {'lmfdb_iso': '1248.a', 'p': 47, 'prec': 20, 'unit': 48237824054768403351823461405703, 'val': 1}
  • id: 31140
    {'lmfdb_iso': '1248.a', 'p': 53, 'prec': 20, 'unit': 256310135290448253761007756638897, 'val': 1}
  • id: 31141
    {'lmfdb_iso': '1248.a', 'p': 59, 'prec': 20, 'unit': 2699296950666325337969945425751744, 'val': 1}
  • id: 31146
    {'lmfdb_iso': '1248.a', 'p': 61, 'prec': 20, 'unit': 498345123872633216724699886457319, 'val': 1}
  • id: 31129
    {'lmfdb_iso': '1248.a', 'p': 67, 'prec': 20, 'unit': 25950589930961851086112694948611795, 'val': 1}
  • id: 31144
    {'lmfdb_iso': '1248.a', 'p': 71, 'prec': 20, 'unit': 129311474450162278546361263579679549, 'val': 1}
  • id: 31142
    {'lmfdb_iso': '1248.a', 'p': 73, 'prec': 20, 'unit': 221907845405765928206194798131638227, 'val': 1}
  • id: 31136
    {'lmfdb_iso': '1248.a', 'p': 79, 'prec': 20, 'unit': 538077891773331288854446822640304460, 'val': 1}
  • id: 31128
    {'lmfdb_iso': '1248.a', 'p': 83, 'prec': 20, 'unit': 1880314388549396047573190168063702533, 'val': 1}
  • id: 31143
    {'lmfdb_iso': '1248.a', 'p': 89, 'prec': 20, 'unit': 1418889149082348543317419517872759571, 'val': 1}
  • id: 31127
    {'lmfdb_iso': '1248.a', 'p': 97, 'prec': 20, 'unit': 33833322118998253319901985440225578407, 'val': 1}