Elliptic curve data - 277200.ie4

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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': '277200ie', 'Clabel': '277200ie3', 'Cnumber': 3, 'abc_quality': 1.0334030036012496, 'absD': 1196629673269020120900000000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9240, 'ainvs': [0, 0, 0, 1362335325, 48942751333250], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 277200, 'degree': 377487360, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.4539658263573199242774656610', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 212, 'isogeny_degrees': [1, 2, 4], 'jinv': [11986661998777424518222, 51295853620928503125], 'lmfdb_iso': '277200.ie', 'lmfdb_label': '277200.ie4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 6054824, 14499537676], 'min_quad_twist_disc': 60, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0-4.c.1.2', '40.12.0.s.1', '120.24.0.?', '616.12.0.?', '1848.24.0.?', '3080.24.0.?', '9240.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.7547605179322145825707384890', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4645558102929316909803339313', 'prec': 100}, 'szpiro_ratio': 6.109437353950094, '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, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, 0, 1, -1, -2, -6, 4, 8, 6, -4, -2, 6, 12, 0, 2, 4, -2, -8, -8, -2, -12, 8, -18, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 277200, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '277200.ie', 'trace_hash': 328378330418387976}
• 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': '0.00013531141575242943465911058923', 'prec': 113}, 'conductor': 277200, 'gens': [[949399, 925792182, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '8.7547605179322145825707384890', 'prec': 100}], 'lmfdb_label': '277200.ie4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.019560740646805125694141592838', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.2199807959757454862621897261003279532', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-24770, 0, 1]], 'xcoord_integral_points': [-24770, 949399]}
• lmfdb_label 277200.ie4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11812663
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [4]}
  • id: 11812664
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '277200.ie4', 'torsion': [4]}
  • id: 11812662
    {'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [2, 2]}
  • id: 11812665
    {'degree': 4, 'field': [100, 0, -10, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [2, 4]}
  • id: 11812669
    {'degree': 8, 'field': [-29106, 18900, 28998, 4248, 360, 378, 40, -4, 1], 'lmfdb_label': '277200.ie4', 'torsion': [6]}
  • id: 11812666
    {'degree': 8, 'field': [361, 0, 252, 0, 74, 0, -12, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [2, 4]}
  • id: 11812667
    {'degree': 8, 'field': [10404, 0, -26304, 0, -1388, 0, 32, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [8]}
  • id: 11812668
    {'degree': 8, 'field': [25600, 0, -4800, 0, 1060, 0, 30, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [8]}
  • id: 11812670
    {'degree': 16, 'field': [14641, 0, 14036, 0, 10310, 0, 3984, 0, 1019, 0, -336, 0, -10, 0, -4, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [4, 4]}
  • id: 11812673
    {'degree': 16, 'field': [4202500, 0, 29010000, 0, -4056500, 0, 730400, 0, -17400, 0, -2980, 0, 496, 0, 12, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [2, 6]}
  • id: 11812675
    {'degree': 16, 'field': [36905625, 0, 2187000, 0, -1510650, 0, 97200, 0, 78975, 0, 720, 0, 270, 0, 0, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [12]}
  • id: 11812674
    {'degree': 16, 'field': [64352484, 0, -213799968, 0, -23710580, 0, 1272864, 0, -199560, 0, -18524, 0, 1968, 0, -60, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [12]}
  • id: 11812671
    {'degree': 16, 'field': [108243216, 0, 273666816, 0, 706341168, 0, -35844096, 0, 2757868, 0, -8192, 0, 2412, 0, -32, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [2, 8]}
  • id: 11812672
    {'degree': 16, 'field': [1475789056, 0, -195767936, 0, 19208000, 0, 1100736, 0, -139936, 0, 5616, 0, 500, 0, -26, 0, 1], 'lmfdb_label': '277200.ie4', 'torsion': [2, 8]}
• 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: 6865690
    {'conductor': 277200, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '277200.ie4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6865691
    {'conductor': 277200, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '277200.ie4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6865692
    {'conductor': 277200, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '277200.ie4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6865693
    {'conductor': 277200, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '277200.ie4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 6865694
    {'conductor': 277200, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '277200.ie4', 'prime': 11, '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: 3413725
    {'adelic_gens': [[5281, 6168, 5724, 6193], [9233, 8, 9232, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [5008, 393, 4227, 7294], [2521, 6168, 3924, 6193], [3079, 0, 0, 9239], [7, 6, 9234, 9235], [4304, 9237, 3075, 6158], [3464, 1917, 381, 6512]], 'adelic_image': '9240.48.0.?', 'conductor': 277200, 'lmfdb_label': '277200.ie4', 'prime': 0}
  • id: 987397
    {'conductor': 277200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '277200.ie4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 277200.ie does not appear in ec_padic