Elliptic curve data - 285318.x1

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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': '285318x', 'Clabel': '285318x1', 'Cnumber': 1, 'abc_quality': 0.9038831403576719, 'absD': 292347021206592, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 3144, 'ainvs': [1, -1, 1, -77342, -8218515], 'analytic_rank': 2, 'bad_primes': [2, 3, 11, 131], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 285318, 'degree': 3317760, 'elladic_images': ['8.6.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6172220344585594168596793379', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2], 'jinv': [39616946929, 226368], 'lmfdb_iso': '285318.x', 'lmfdb_label': '285318.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -71, -259], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.d.1', '786.6.0.?', '3144.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 11, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '5.4061498211172024635522647702', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.13103174627468070086891506954', 'prec': 107}, 'szpiro_ratio': 3.612791093789922, '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, 0, 1, -4, 0, 4, 1, 0, -4, 0, 0, -6, 4, 0, 1, -2, 0, -4, -4], 'aplist': [1, 0, -4, 4, 0, -6, -2, -4, -4, -6, -2, -8, 6, -12, 8, -12, 8, 6, -12, -4, 14, -10, 4, -10, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 285318, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '285318.x', 'trace_hash': 1566865307787694321}
• 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': '0.039382092584908242496059611115', 'prec': 107}, 'conductor': 285318, 'gens': [[-157, 267, 1], [-169, 21, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0423271121205809573016923062', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.8786966789922384628141822704', 'prec': 100}], 'lmfdb_label': '285318.x1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.28638190696159437702783478773', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '18.578681941099521123075958741517563267', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-151, 75, 1]], 'xcoord_integral_points': [-169, -157, -151, 333, 437, 1301]}
• lmfdb_label 285318.x1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12130652
    {'degree': 2, 'field': [-98, -1, 1], 'lmfdb_label': '285318.x1', 'torsion': [2, 2]}
  • id: 12130653
    {'degree': 4, 'field': [2946, 104, -103, -2, 1], 'lmfdb_label': '285318.x1', 'torsion': [4]}
  • id: 12130656
    {'degree': 8, 'field': [18582, 27867, 5103, 2994, 138, 96, 4, -1, 1], 'lmfdb_label': '285318.x1', 'torsion': [6]}
  • id: 12130655
    {'degree': 8, 'field': [1160274, -1305264, 590269, -121562, 6881, 1372, -193, -2, 1], 'lmfdb_label': '285318.x1', 'torsion': [2, 4]}
  • id: 12130654
    {'degree': 8, 'field': [5763652, -6613540, 2246360, -193606, -24161, 3232, 8, -2, 1], 'lmfdb_label': '285318.x1', 'torsion': [2, 4]}
  • id: 12130657
    {'degree': 16, 'field': [1209718416384, 0, -78210137088, 0, -2021625216, 0, 124127424, 0, 5140548, 0, 38496, 0, -2108, 0, -64, 0, 1], 'lmfdb_label': '285318.x1', 'torsion': [8]}
  • id: 12130658
    {'degree': 16, 'field': [1686341182464, 0, -280352556432, 0, 12526638264, 0, -474697233, 0, 14515011, 0, -442233, 0, 10353, 0, -147, 0, 1], 'lmfdb_label': '285318.x1', '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: 7067870
    {'conductor': 285318, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '285318.x1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 7067871
    {'conductor': 285318, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '285318.x1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7067872
    {'conductor': 285318, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '285318.x1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7067873
    {'conductor': 285318, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '285318.x1', 'prime': 131, '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: 3463094
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [1573, 4, 2, 9], [1969, 1180, 392, 2751], [3141, 4, 3140, 5], [2098, 1, 2095, 0], [266, 1, 1439, 0]], 'adelic_image': '3144.12.0.?', 'conductor': 285318, 'lmfdb_label': '285318.x1', 'prime': 0}
  • id: 1012753
    {'conductor': 285318, 'elladic_image': '8.6.0.4', 'lmfdb_label': '285318.x1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 285318.x does not appear in ec_padic