Elliptic curve data - 377520.e4

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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': '377520e', 'Clabel': '377520e3', 'Cnumber': 3, 'abc_quality': 1.0213953201021033, 'absD': 27636351600000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3432, 'ainvs': [0, -1, 0, 75464, 528640], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 377520, 'degree': 3932160, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8442678616112127657125924971', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [26198797244, 15234375], 'lmfdb_iso': '377520.e', 'lmfdb_label': '377520.e4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 624, 624], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '78.6.0.?', '88.12.0.?', '104.12.0.?', '132.12.0.?', '156.12.0.?', '264.24.0.?', '312.24.0.?', '572.12.0.?', '1144.24.0.?', '1716.24.0.?', '3432.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 4719], [3, 4, 125840], [5, 6, 75504], [11, 62, 3120], [13, 14, 29040]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.067697574745406402500593940235', 'prec': 107}, 'szpiro_ratio': 3.528267750281194, '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, -4, 0, 1, 0, 0, 0, -1, 0, 1, 0, 6, 0, 0, 0], 'aplist': [0, -1, -1, -4, 0, -1, 6, 0, 8, -6, 4, -2, 10, -4, 8, -2, -12, 2, 16, 8, 6, -16, 4, -2, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 377520, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '377520.e', 'trace_hash': 1517552563052166536}
• 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': '0.025008594749343573242224118647', 'prec': 107}, 'conductor': 377520, 'gens': [], 'heights': [], 'lmfdb_label': '377520.e4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.22569936101942966248239739416', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8055948881554372998591791533019777567', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-7, 0, 1]], 'xcoord_integral_points': [-7]}
• lmfdb_label 377520.e4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 15643200
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '377520.e4', 'torsion': [4]}
  • id: 15643199
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '377520.e4', 'torsion': [2, 2]}
  • id: 15643201
    {'degree': 2, 'field': [36, -1, 1], 'lmfdb_label': '377520.e4', 'torsion': [4]}
  • id: 15643202
    {'degree': 4, 'field': [108, -63, 19, -1, 1], 'lmfdb_label': '377520.e4', 'torsion': [2, 4]}
  • id: 15643206
    {'degree': 8, 'field': [-3557763, 0, -910404, 0, -6534, 0, 0, 0, 1], 'lmfdb_label': '377520.e4', 'torsion': [6]}
  • id: 15643204
    {'degree': 8, 'field': [-200, 280, 98, -158, 37, 14, -4, -4, 1], 'lmfdb_label': '377520.e4', 'torsion': [8]}
  • id: 15643205
    {'degree': 8, 'field': [10299, -17580, 17816, -432, 117, 116, -34, -4, 1], 'lmfdb_label': '377520.e4', 'torsion': [8]}
  • id: 15643203
    {'degree': 8, 'field': [3651921, 0, 0, 0, -1326, 0, 0, 0, 1], 'lmfdb_label': '377520.e4', 'torsion': [2, 4]}
  • id: 15643211
    {'degree': 16, 'field': [-1436709474, -1054147284, 384488370, 310493196, -126478152, -4226202, 13264722, -1452762, -76923, -14208, -49452, 906, 4168, -26, -94, -4, 1], 'lmfdb_label': '377520.e4', 'torsion': [12]}
  • id: 15643209
    {'degree': 16, 'field': [331776, 0, -312768, 0, 114372, 0, 8520, 0, -6791, 0, 160, 0, 162, 0, -8, 0, 1], 'lmfdb_label': '377520.e4', 'torsion': [2, 8]}
  • id: 15643207
    {'degree': 16, 'field': [517016644, 0, 475829960, 0, -59024288, 0, 8953988, 0, 2659909, 0, 6452, 0, -3170, 0, 8, 0, 1], 'lmfdb_label': '377520.e4', 'torsion': [4, 4]}
  • id: 15643208
    {'degree': 16, 'field': [3576238363, -237670796, 1450751820, -132755200, 265150923, -27001164, 30683662, -3614020, 2534658, -298244, 140752, -13944, 4935, -356, 102, -4, 1], 'lmfdb_label': '377520.e4', 'torsion': [2, 8]}
  • id: 15643212
    {'degree': 16, 'field': [99179645184, 0, -7754787072, 0, 20620855584, 0, -47869056, 0, 3184029, 0, -73188, 0, 3834, 0, 0, 0, 1], 'lmfdb_label': '377520.e4', 'torsion': [12]}
  • id: 15643210
    {'degree': 16, 'field': [80794610536000, -80504468998720, 35923050162336, -10112713841472, 2170445533680, -383838286224, 55217662984, -6435350656, 588527034, -32119008, -183354, 191448, -23140, 994, 72, -4, 1], 'lmfdb_label': '377520.e4', '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: 9339916
    {'conductor': 377520, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '377520.e4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 9339917
    {'conductor': 377520, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '377520.e4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9339918
    {'conductor': 377520, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '377520.e4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9339919
    {'conductor': 377520, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '377520.e4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9339920
    {'conductor': 377520, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '377520.e4', '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: 4011882
    {'adelic_gens': [[7, 6, 3426, 3427], [3425, 8, 3424, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1517, 3080, 1342, 3387], [892, 2497, 1463, 2190], [1915, 1914, 2002, 595], [2608, 627, 1045, 2498], [2495, 0, 0, 3431]], 'adelic_image': '3432.48.0.?', 'conductor': 377520, 'lmfdb_label': '377520.e4', 'prime': 0}
  • id: 1292784
    {'conductor': 377520, 'elladic_image': '4.6.0.1', 'lmfdb_label': '377520.e4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 377520.e does not appear in ec_padic