Elliptic curve data - 478800.z1

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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': '478800z', 'Clabel': '478800z4', 'Cnumber': 4, 'abc_quality': 0.8903179969915103, 'absD': 319213470240000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 15960, 'ainvs': [0, 0, 0, -1035075, -404414750], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 7, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 478800, 'degree': 7077888, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2342579693541902708118044133', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 4], 'jinv': [5257286722802, 13683705], 'lmfdb_iso': '478800.z', 'lmfdb_label': '478800.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -4600, -121360], 'min_quad_twist_disc': 60, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.2', '140.12.0.?', '760.12.0.?', '840.24.0.?', '1064.12.0.?', '2280.24.0.?', '3192.24.0.?', '5320.24.0.?', '15960.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 17, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '2.9481448612489138576247034878', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1575], [3, 8, 53200], [5, 18, 19152], [7, 8, 68400], [19, 20, 25200]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.24484795328980203751467268356', 'prec': 103}, 'szpiro_ratio': 4.064790953521386, '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, -4, 0, -2, 0, 0, 0, -6, 0, -1, 0], 'aplist': [0, 0, 0, -1, -4, -2, -6, -1, 0, -2, -8, 10, -2, 4, 0, -6, 0, 10, -4, -8, -14, 8, -12, -10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 478800, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '478800.z', 'trace_hash': 396040564227337879}
• 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': '0.011464316981091966073712538492', 'prec': 107}, 'conductor': 478800, 'gens': [[-595, 900, 1], [1205, 9900, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0501890217489404400455100186', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.8930705921042124854833186905', 'prec': 100}], 'lmfdb_label': '478800.z1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.14970094262313511079146703067', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '14.122882070992456822621060094955974629', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-610, 0, 1]], 'xcoord_integral_points': [-610, -595, -585, -574, 1205, 1415, 2639, 4805, 35405]}
• lmfdb_label 478800.z1 does not appear in ec_iwasawa
• lmfdb_label 478800.z1 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: 11799110
    {'conductor': 478800, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '478800.z1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 11799111
    {'conductor': 478800, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '478800.z1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 11799112
    {'conductor': 478800, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '478800.z1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 11799113
    {'conductor': 478800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '478800.z1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 11799114
    {'conductor': 478800, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '478800.z1', '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: 4600631
    {'adelic_gens': [[7, 6, 15954, 15955], [13957, 13964, 13918, 5979], [1, 0, 8, 1], [15953, 8, 15952, 9], [1, 8, 0, 1], [1, 4, 4, 17], [13968, 5993, 1987, 1974], [9572, 15959, 3169, 15954], [5312, 15957, 5315, 15958], [4201, 8, 844, 33], [13688, 3, 4565, 2]], 'adelic_image': '15960.48.0.?', 'conductor': 478800, 'lmfdb_label': '478800.z1', 'prime': 0}
  • id: 1587727
    {'conductor': 478800, 'elladic_image': '4.6.0.1', 'lmfdb_label': '478800.z1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 478800.z does not appear in ec_padic