Elliptic curve data - 478800.pj1

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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': '478800pj', 'Clabel': '478800pj6', 'Cnumber': 6, 'abc_quality': 1.0583334848509944, 'absD': 278160318922752000000, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 23940, 'ainvs': [0, 0, 0, -35232157875, -2545405502660750], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 19], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 478800, 'degree': 573308928, 'elladic_images': ['2.3.0.1', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.3094055171109823485233277501', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 18, 'iso_nlabel': 399, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [103665426767620308239307625, 5961940992], 'lmfdb_iso': '478800.pj', 'lmfdb_label': '478800.pj1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -9786711, -11785100294], 'min_quad_twist_disc': 60, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '9.12.0.a.1', '18.36.0.a.1', '28.6.0.a.1', '60.24.0-6.a.1.4', '84.24.0.?', '180.72.0.?', '210.24.0.?', '228.24.0.?', '252.72.1.?', '420.48.0.?', '630.72.0.?', '684.72.1.?', '1140.48.0.?', '1197.36.0.?', '1260.144.1.?', '1596.48.1.?', '2394.108.2.?', '3420.144.1.?', '4788.432.21.?', '7980.96.1.?', '11970.216.2.?', '23940.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1575], [3, 8, 53200], [5, 14, 19152], [7, 8, 68400], [19, 20, 25200]], 'sha': 36, 'sha_primes': [2, 3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2622332359999320061080933436', 'prec': 100}, 'szpiro_ratio': 6.458370763689036, '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, 6, 0, 4, 0, 0, 0, 0, 0, -1, 0], 'aplist': [0, 0, 0, 1, 6, 4, 0, -1, -6, -6, 4, -2, 6, 8, -12, 6, -12, -10, 14, -12, -2, 10, -12, -18, -8], 'class_deg': 18, 'class_size': 6, 'conductor': 478800, 'isogeny_matrix': [[1, 2, 3, 6, 9, 18], [2, 1, 6, 3, 18, 9], [3, 6, 1, 2, 3, 6], [6, 3, 2, 1, 6, 3], [9, 18, 3, 6, 1, 2], [18, 9, 6, 3, 2, 1]], 'lmfdb_iso': '478800.pj', 'trace_hash': 69521826191218996}
• 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': '0.00018067494337163346577837527695', 'prec': 113}, 'conductor': 478800, 'gens': [], 'heights': [], 'lmfdb_label': '478800.pj1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.011019572430946455062187929697', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '36.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1736368601125790579101237528354281385', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-108370, 0, 1]], 'xcoord_integral_points': [-108370]}
• lmfdb_label 478800.pj1 does not appear in ec_iwasawa
• lmfdb_label 478800.pj1 does not appear in ec_torsion_growth
• 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: 11802580
    {'conductor': 478800, 'conductor_valuation': 4, 'discriminant_valuation': 30, 'j_denominator_valuation': 18, 'kodaira_symbol': -26, 'lmfdb_label': '478800.pj1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 11802581
    {'conductor': 478800, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '478800.pj1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 11802582
    {'conductor': 478800, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '478800.pj1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 11802583
    {'conductor': 478800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '478800.pj1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 11802584
    {'conductor': 478800, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '478800.pj1', 'prime': 19, '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: 4600615
    {'adelic_gens': [[1, 36, 0, 1], [14354, 19125, 7925, 6794], [1, 0, 36, 1], [11699, 9540, 9250, 11059], [14363, 0, 0, 23939], [2551, 14400, 13670, 19411], [3436, 9585, 9875, 18166], [23905, 36, 23904, 37], [19, 36, 3240, 6139], [1, 18, 14, 253]], 'adelic_image': '23940.864.21.?', 'conductor': 478800, 'lmfdb_label': '478800.pj1', 'prime': 0}
  • id: 1587713
    {'conductor': 478800, 'elladic_image': '2.3.0.1', 'lmfdb_label': '478800.pj1', 'modell_image': '2B', 'prime': 2}
  • id: 1587714
    {'conductor': 478800, 'elladic_image': '9.12.0.1', 'lmfdb_label': '478800.pj1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 478800.pj does not appear in ec_padic