Elliptic curve data - 117648.bg4

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '117648x', 'Clabel': '117648x4', 'Cnumber': 4, 'abc_quality': 0.9979360354745357, 'absD': 83731064844587618009088, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 9804, 'ainvs': [0, 0, 0, 4905285, -13279155478], 'analytic_rank': 1, 'bad_primes': [2, 3, 19, 43], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 117648, 'degree': 7962624, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0802779701704741231875448437', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'intrinsic_torsion': 1, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4371484788393482375, 28041364201746432], 'lmfdb_iso': '117648.bg', 'lmfdb_label': '117648.bg4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 34064, -7681858], 'min_quad_twist_disc': 12, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.24.0.b.1', '12.48.0-6.b.1.1', '3268.6.0.?', '9804.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.652012184888733285002806816', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 304], [19, 20, 6192], [43, 44, 2736]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8378246452764739680726901038', 'prec': 100}, 'szpiro_ratio': 5.151155285183298, '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, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, -1, 0], 'aplist': [0, 0, 0, 4, 0, 2, 6, -1, 0, -6, 4, 2, 0, -1, 0, -12, 6, -10, -8, -12, 14, -8, 0, -6, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 117648, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '117648.bg', 'trace_hash': 1376273602466969138}
• 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': '0.0021110793112848803137732789321', 'prec': 110}, 'conductor': 117648, 'gens': [[704449, 591956001, 4]], 'heights': [{'__RealLiteral__': 0, 'data': '10.652012184888733285002806816', 'prec': 100}], 'lmfdb_label': '117648.bg4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.053919112139054301718253986755', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.1895526320574149407396807917494819073', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[1702, 0, 1]], 'xcoord_integral_points': [1702]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 1, 0], '7': [1, 0], '11': [1, 3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '117648.bg4'}
• ec_torsion_growth •

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

  
  
  • id: 5391085
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '117648.bg4', 'torsion': [2, 2]}
  • id: 5391086
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [6]}
  • id: 5391087
    {'degree': 4, 'field': [-48, 0, -25, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [4]}
  • id: 5391088
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [2, 6]}
  • id: 5391089
    {'degree': 6, 'field': [-1083, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [6]}
  • id: 5391091
    {'degree': 8, 'field': [2304, 0, -1200, 0, 673, 0, 25, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [2, 4]}
  • id: 5391092
    {'degree': 8, 'field': [2304, 0, 3121, 0, 480, 0, -48, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [12]}
  • id: 5391090
    {'degree': 8, 'field': [47089, -434, -10798, 1630, 439, -106, 56, -4, 1], 'lmfdb_label': '117648.bg4', 'torsion': [2, 4]}
  • id: 5391093
    {'degree': 12, 'field': [1175056, 0, 385944, 0, 42585, 0, -1147, 0, -336, 0, -3, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [6, 6]}
  • id: 5391096
    {'degree': 16, 'field': [5308416, 0, -7190784, 0, 8634721, 0, -1719264, 0, 377904, 0, 29282, 0, 1824, 0, 48, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [2, 12]}
  • id: 5391095
    {'degree': 16, 'field': [8412121, -2609568, -7504488, 1048848, 3336634, -121248, -853896, -8688, 137979, 2592, -14856, -144, 1078, 0, -48, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [2, 12]}
  • id: 5391094
    {'degree': 16, 'field': [510601710096, 0, 159074636832, 0, -43647428568, 0, 1361562504, 0, 12393601, 0, -1236920, 0, 26091, 0, -248, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [8]}
  • id: 5391097
    {'degree': 18, 'field': [173570457804231168, 31792153732273152, 2911615985009664, -1948133229975360, 223906408451712, -17372733098400, 3994720473924, -952578208800, 148166252352, -14847441624, 1202833152, -79707888, 2154888, 66960, 9072, -2076, 0, 0, 1], 'lmfdb_label': '117648.bg4', 'torsion': [18]}
• 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: 2896247
    {'conductor': 117648, 'conductor_valuation': 4, 'discriminant_valuation': 24, 'j_denominator_valuation': 12, 'kodaira_symbol': -20, 'lmfdb_label': '117648.bg4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2896248
    {'conductor': 117648, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '117648.bg4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2896249
    {'conductor': 117648, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '117648.bg4', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2896250
    {'conductor': 117648, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '117648.bg4', 'prime': 43, 'reduction_type': -1, '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: 2432981
    {'adelic_gens': [[6526, 9801, 6563, 8], [6709, 12, 1038, 73], [4561, 12, 7758, 73], [9793, 12, 9792, 13], [1, 12, 0, 1], [1, 6, 6, 37], [1, 0, 12, 1], [5709, 8984, 5746, 8995], [11, 2, 9754, 9795]], 'adelic_image': '9804.96.1.?', 'conductor': 117648, 'lmfdb_label': '117648.bg4', 'prime': 0}
  • id: 463638
    {'conductor': 117648, 'elladic_image': '2.3.0.1', 'lmfdb_label': '117648.bg4', 'modell_image': '2B', 'prime': 2}
  • id: 463639
    {'conductor': 117648, 'elladic_image': '3.4.0.1', 'lmfdb_label': '117648.bg4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 6148253
    {'lmfdb_iso': '117648.bg', 'p': 7, 'prec': 20, 'unit': 7657163918214609, 'val': 1}
  • id: 6148257
    {'lmfdb_iso': '117648.bg', 'p': 13, 'prec': 20, 'unit': 1349719714766198627321, 'val': 1}
  • id: 6148259
    {'lmfdb_iso': '117648.bg', 'p': 17, 'prec': 20, 'unit': 219527289277320763436437, 'val': 1}
  • id: 6148256
    {'lmfdb_iso': '117648.bg', 'p': 29, 'prec': 20, 'unit': 2206629648137595685283099271, 'val': 1}
  • id: 6148264
    {'lmfdb_iso': '117648.bg', 'p': 31, 'prec': 20, 'unit': 17080887658530493051189326305, 'val': 1}
  • id: 6148252
    {'lmfdb_iso': '117648.bg', 'p': 37, 'prec': 20, 'unit': 462315564596808569198234486593, 'val': 1}
  • id: 6148260
    {'lmfdb_iso': '117648.bg', 'p': 53, 'prec': 20, 'unit': 470783121006788118175843438944598, 'val': 1}
  • id: 6148262
    {'lmfdb_iso': '117648.bg', 'p': 59, 'prec': 20, 'unit': 142158820714496958604361775092410, 'val': 1}
  • id: 6148263
    {'lmfdb_iso': '117648.bg', 'p': 61, 'prec': 20, 'unit': 3365735786685462111259566438806719, 'val': 1}
  • id: 6148251
    {'lmfdb_iso': '117648.bg', 'p': 67, 'prec': 20, 'unit': 21533399246166112743706737436739137, 'val': 1}
  • id: 6148255
    {'lmfdb_iso': '117648.bg', 'p': 71, 'prec': 20, 'unit': 120291107036424658451557490317299432, 'val': 1}
  • id: 6148254
    {'lmfdb_iso': '117648.bg', 'p': 73, 'prec': 20, 'unit': 48333972126306509165436818113607262, 'val': 1}
  • id: 6148258
    {'lmfdb_iso': '117648.bg', 'p': 79, 'prec': 20, 'unit': 1060276135828397876228045721616278124, 'val': 1}
  • id: 6148261
    {'lmfdb_iso': '117648.bg', 'p': 89, 'prec': 20, 'unit': 6148926887057467768741060858703908264, 'val': 1}
  • id: 6148250
    {'lmfdb_iso': '117648.bg', 'p': 97, 'prec': 20, 'unit': 20725534738720889437808177745126551597, 'val': 1}