Elliptic curve data - 47040.gp3

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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': '47040dc', 'Clabel': '47040dc7', 'Cnumber': 7, 'abc_quality': 1.0450039140149439, 'absD': 11064699901139704369643520, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 840, 'ainvs': [0, 1, 0, -63825505, 253221862655], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 47040, 'degree': 10616832, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5149408516780232973552807589', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 171, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [-932348627918877961, 358766164249920], 'lmfdb_iso': '47040.gp', 'lmfdb_label': '47040.gp3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -20353, -1443724], 'min_quad_twist_disc': -56, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.2', '20.12.0.h.1', '24.96.0-12.c.2.2', '56.12.0-4.c.1.1', '60.96.1.m.2', '120.192.1.?', '168.192.1.?', '280.24.0.?', '840.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5022650063104486806767562050', 'prec': 100}, 'szpiro_ratio': 6.138106686548813, '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, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 6, 0, 8, 0], 'aplist': [0, 1, 1, 0, 0, 2, 6, 8, 0, -6, 4, 10, 6, 4, 0, 6, -12, -10, 4, 12, 10, 8, 12, 6, 10], 'class_deg': 12, 'class_size': 8, 'conductor': 47040, 'isogeny_matrix': [[1, 2, 4, 3, 4, 6, 12, 12], [2, 1, 2, 6, 2, 3, 6, 6], [4, 2, 1, 12, 4, 6, 12, 3], [3, 6, 12, 1, 12, 2, 4, 4], [4, 2, 4, 12, 1, 6, 3, 12], [6, 3, 6, 2, 6, 1, 2, 2], [12, 6, 12, 4, 3, 2, 1, 4], [12, 6, 3, 4, 12, 2, 4, 1]], 'lmfdb_iso': '47040.gp', 'trace_hash': 1846664133237513502}
• 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': '0.00088503647124774133312562110507', 'prec': 113}, 'conductor': 47040, 'gens': [], 'heights': [], 'lmfdb_label': '47040.gp3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.067543615260578638541355984285', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.8631402987616619749776308685149598095', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-9511, 0, 1]], 'xcoord_integral_points': [-9511]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [5, 0], '5': [3, 0], '7': 'a'}, 'iwp0': 5, 'lmfdb_label': '47040.gp3'}
• ec_torsion_growth •

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

  
  
  • id: 2294212
    {'degree': 2, 'field': [-70, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [4]}
  • id: 2294214
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [6]}
  • id: 2294211
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [2, 2]}
  • id: 2294213
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [4]}
  • id: 2294217
    {'degree': 4, 'field': [49, 0, -56, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [12]}
  • id: 2294215
    {'degree': 4, 'field': [81, 0, 38, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [2, 4]}
  • id: 2294218
    {'degree': 4, 'field': [196, 0, -14, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [12]}
  • id: 2294216
    {'degree': 4, 'field': [2209, 0, -74, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [2, 6]}
  • id: 2294219
    {'degree': 6, 'field': [2969, 1260, 588, -30, 42, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [12]}
  • id: 2294222
    {'degree': 8, 'field': [9, 0, 30, 0, 19, 0, 4, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [8]}
  • id: 2294221
    {'degree': 8, 'field': [256, 0, -406, 0, 81, 0, 14, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [8]}
  • id: 2294220
    {'degree': 8, 'field': [3745, 3500, 1010, 200, 56, -64, 26, -4, 1], 'lmfdb_label': '47040.gp3', 'torsion': [2, 4]}
  • id: 2294223
    {'degree': 8, 'field': [6561, 0, -3078, 0, 1363, 0, -38, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [2, 12]}
  • id: 2294225
    {'degree': 12, 'field': [5470921, 0, 5608344, 0, 406140, 0, 55690, 0, 2940, 0, 84, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [2, 12]}
  • id: 2294224
    {'degree': 12, 'field': [8814961, -3740940, -158172, -919020, 258846, 123480, -17858, 0, 1176, -60, -42, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [3, 12]}
  • id: 2294231
    {'degree': 16, 'field': [81, 0, -270, 0, 729, 0, -498, 0, 232, 0, -16, 0, -3, 0, -4, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [24]}
  • id: 2294230
    {'degree': 16, 'field': [6561, 0, -23328, 0, 40905, 0, -38448, 0, 18144, 0, -4272, 0, 505, 0, -32, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [24]}
  • id: 2294227
    {'degree': 16, 'field': [19089, -45612, 38760, -17316, -15866, 12568, 32024, -27132, 10255, -5224, 3352, -1132, 238, -60, 32, -8, 1], 'lmfdb_label': '47040.gp3', 'torsion': [2, 8]}
  • id: 2294228
    {'degree': 16, 'field': [230400, 0, -76800, 0, 88960, 0, -9600, 0, -4284, 0, 436, 0, 141, 0, -24, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [2, 8]}
  • id: 2294226
    {'degree': 16, 'field': [2595321, 3885732, 2908872, -248148, 176638, 169272, 67320, 30340, -6689, -1960, 2600, -268, -2, -28, 32, -8, 1], 'lmfdb_label': '47040.gp3', 'torsion': [4, 4]}
  • id: 2294229
    {'degree': 16, 'field': [3723526, 18222680, 40494968, 18316620, -224560, -1272460, -701462, -26880, 96739, 18900, 7542, -1400, -80, -140, 12, 0, 1], 'lmfdb_label': '47040.gp3', 'torsion': [2, 12]}
  • id: 2294232
    {'degree': 18, 'field': [912754116, -2117011464, 1172208780, -91074492, 357236910, -401034024, 166879753, -50917536, 14292552, -3249792, -123537, -108972, -84326, -3744, -1893, -72, 12, 0, 1], 'lmfdb_label': '47040.gp3', '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: 1122546
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 24, 'j_denominator_valuation': 6, 'kodaira_symbol': -18, 'lmfdb_label': '47040.gp3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1122547
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '47040.gp3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1122548
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '47040.gp3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1122549
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '47040.gp3', 'prime': 7, 'reduction_type': 0, '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: 1977680
    {'adelic_gens': [[599, 816, 468, 551], [1, 12, 12, 145], [352, 21, 555, 466], [159, 32, 4, 331], [15, 106, 374, 11], [141, 284, 8, 453], [214, 3, 255, 34], [817, 24, 816, 25], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '840.384.5.?', 'conductor': 47040, 'lmfdb_label': '47040.gp3', 'prime': 0}
  • id: 203612
    {'conductor': 47040, 'elladic_image': '4.6.0.1', 'lmfdb_label': '47040.gp3', 'modell_image': '2B', 'prime': 2}
  • id: 203613
    {'conductor': 47040, 'elladic_image': '3.4.0.1', 'lmfdb_label': '47040.gp3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 47040.gp does not appear in ec_padic