Elliptic curve data - 139650.ef4

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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': '139650ha', 'Clabel': '139650ha1', 'Cnumber': 1, 'abc_quality': 0.9574479119060725, 'absD': 228137881860000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 31920, 'ainvs': [1, 0, 1, -12378651, -16764259802], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 19], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 139650, 'degree': 8847360, 'elladic_images': ['16.24.0.14'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6181334391850793663122803219', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 109, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [114113060120923921, 124104960], 'lmfdb_iso': '139650.ef', 'lmfdb_label': '139650.ef4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -10105, 390137], 'min_quad_twist_disc': -35, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.6', '24.24.0-8.n.1.8', '48.48.0-48.h.1.5', '76.12.0.?', '140.12.0.?', '152.24.0.?', '280.24.0.?', '304.48.0.?', '456.48.0.?', '560.48.0.?', '840.48.0.?', '912.96.0.?', '1330.6.0.?', '1680.96.0.?', '2660.24.0.?', '5320.48.0.?', '10640.96.0.?', '15960.96.0.?', '31920.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.84045940844037252645922428356', 'prec': 103}, 'szpiro_ratio': 5.115944445279047, '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, -1, 1, 1, 0, -1, 0, -1, 1, 0, 4, 1, 6, 0, 0, 1, 2, -1, 1, 0], 'aplist': [-1, 1, 0, 0, 4, 6, 2, 1, 8, -2, -8, 10, -10, -4, -8, 10, 4, 10, 4, 16, 10, 8, 12, 6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 139650, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '139650.ef', 'trace_hash': 1477457256731958290}
• 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': '0.0053200803180211120496216376836', 'prec': 110}, 'conductor': 139650, 'gens': [], 'heights': [], 'lmfdb_label': '139650.ef4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.080488022525650129604744236132', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8634250812312062210277233343506062695', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-2033, 1016, 1]], 'xcoord_integral_points': [-2033]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': [1, 0], '5': 'a', '7': 'a', '19': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '139650.ef4'}
• ec_torsion_growth •

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

  
  
  • id: 6315149
    {'degree': 2, 'field': [-166, -1, 1], 'lmfdb_label': '139650.ef4', 'torsion': [2, 2]}
  • id: 6315150
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '139650.ef4', 'torsion': [4]}
  • id: 6315151
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '139650.ef4', 'torsion': [4]}
  • id: 6315152
    {'degree': 4, 'field': [16, 0, 27, 0, 1], 'lmfdb_label': '139650.ef4', 'torsion': [2, 4]}
  • id: 6315154
    {'degree': 4, 'field': [81, -9, -8, -1, 1], 'lmfdb_label': '139650.ef4', 'torsion': [8]}
  • id: 6315153
    {'degree': 4, 'field': [529, 0, -11, 0, 1], 'lmfdb_label': '139650.ef4', 'torsion': [8]}
  • id: 6315158
    {'degree': 8, 'field': [-17064, -1971, 1512, 917, -455, -7, 7, -4, 1], 'lmfdb_label': '139650.ef4', 'torsion': [6]}
  • id: 6315157
    {'degree': 8, 'field': [256, 0, -432, 0, 713, 0, -27, 0, 1], 'lmfdb_label': '139650.ef4', 'torsion': [2, 8]}
  • id: 6315156
    {'degree': 8, 'field': [62701, -15166, 15932, -1498, 665, 98, -28, -4, 1], 'lmfdb_label': '139650.ef4', 'torsion': [8]}
  • id: 6315155
    {'degree': 8, 'field': [1323576, 1260324, 111393, -71640, 9766, 1100, -178, -2, 1], 'lmfdb_label': '139650.ef4', 'torsion': [2, 4]}
  • id: 6315160
    {'degree': 16, 'field': [256, 0, 0, 0, -21024, 0, 0, 0, 474241, 0, 0, 0, -1314, 0, 0, 0, 1], 'lmfdb_label': '139650.ef4', 'torsion': [2, 8]}
  • id: 6315164
    {'degree': 16, 'field': [589824, 0, -9834524928, 0, -989365760, 0, -27910656, 0, -1446675, 0, -140184, 0, -4182, 0, 0, 0, 1], 'lmfdb_label': '139650.ef4', 'torsion': [2, 6]}
  • id: 6315163
    {'degree': 16, 'field': [1904400, 0, 212427000, 0, 2562637065, 0, 681590850, 0, 60570271, 0, 2336372, 0, 41799, 0, 338, 0, 1], 'lmfdb_label': '139650.ef4', 'torsion': [16]}
  • id: 6315166
    {'degree': 16, 'field': [7851204, 0, 54645363, 0, 19599330, 0, 3916181, 0, 473075, 0, 38729, 0, 2083, 0, 70, 0, 1], 'lmfdb_label': '139650.ef4', 'torsion': [12]}
  • id: 6315165
    {'degree': 16, 'field': [1435955236, 0, -216226672, 0, -708512, 0, 8167551, 0, 292110, 0, 19131, 0, -287, 0, 38, 0, 1], 'lmfdb_label': '139650.ef4', 'torsion': [12]}
  • id: 6315162
    {'degree': 16, 'field': [194673842244, -96229244664, 96872726286, -39600632988, 17312768265, -5547320280, 1422760836, -330898392, 60938806, -9585592, 1571854, -194884, 24916, -1792, 232, -4, 1], 'lmfdb_label': '139650.ef4', 'torsion': [16]}
  • id: 6315159
    {'degree': 16, 'field': [200310848721, 0, 0, 0, 686302866, 0, 0, 0, 1475731, 0, 0, 0, 1346, 0, 0, 0, 1], 'lmfdb_label': '139650.ef4', 'torsion': [4, 4]}
  • id: 6315161
    {'degree': 16, 'field': [19125838860641060, -1414017074466260, 1828164249059410, -141039310621370, 62251221085445, -3899771460830, 1009718598420, -48356855580, 9795864836, -354341026, 61435822, -1550458, 257040, -4032, 682, -4, 1], 'lmfdb_label': '139650.ef4', 'torsion': [16]}
• 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: 3449420
    {'conductor': 139650, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '139650.ef4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3449421
    {'conductor': 139650, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '139650.ef4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 3449422
    {'conductor': 139650, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '139650.ef4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 3449423
    {'conductor': 139650, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '139650.ef4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3449424
    {'conductor': 139650, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '139650.ef4', 'prime': 19, '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: 2571710
    {'adelic_gens': [[1, 16, 23940, 23941], [5, 4, 31916, 31917], [1, 16, 0, 1], [31905, 16, 31904, 17], [21293, 16, 10384, 31605], [6368, 31915, 45, 14], [1, 0, 16, 1], [4544, 31915, 9165, 14], [15, 2, 31822, 31907], [4001, 16, 12170, 8271], [1688, 1, 28639, 10]], 'adelic_image': '31920.192.1.?', 'conductor': 139650, 'lmfdb_label': '139650.ef4', 'prime': 0}
  • id: 539969
    {'conductor': 139650, 'elladic_image': '16.24.0.14', 'lmfdb_label': '139650.ef4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 139650.ef does not appear in ec_padic