Elliptic curve data - 259200.gp1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '259200gp', 'Clabel': '259200gp1', 'Cnumber': 1, 'abc_quality': 1.0688427426847569, 'absD': 259200, 'adelic_genus': 0, 'adelic_index': 10, 'adelic_level': 40, 'ainvs': [0, 0, 0, -525, -4630], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 259200, 'degree': 117504, 'elladic_images': ['8.2.0.2', '5.5.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.17123762923823345082694425859', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 171, 'isogeny_degrees': [1], 'jinv': [61740000, 1], 'lmfdb_iso': '259200.gp', 'lmfdb_label': '259200.gp1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -2100, 37040], 'min_quad_twist_disc': -8, 'modell_images': ['5S4'], 'modm_images': ['5.5.0.a.1', '8.2.0.b.1', '40.10.0.b.1'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2025], [3, 8, 3200], [5, 10, 10368]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.86754197438345460589831611344', 'prec': 107}, 'szpiro_ratio': 2.4390638876055615, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 5, 0, 0, 0, -6, 0, 4, 0, 0, 0, 7, 0, 2, 0], 'aplist': [0, 0, 0, 5, -6, 4, 7, 2, 0, -2, -4, -10, 9, 0, -3, 10, -12, 0, 2, 16, 5, 15, 6, 3, -13], 'class_deg': 1, 'class_size': 1, 'conductor': 259200, 'isogeny_matrix': [[1]], 'lmfdb_iso': '259200.gp', 'trace_hash': 409184966148072201}
• 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': '0.71001068591433323847461105734', 'prec': 103}, 'conductor': 259200, 'gens': [], 'heights': [], 'lmfdb_label': '259200.gp1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.99737884167185467249209037009', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9895153666874186899683614803727111557', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 259200.gp1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11113627
    {'degree': 3, 'field': [-40, -30, 0, 1], 'lmfdb_label': '259200.gp1', 'torsion': [2]}
  • id: 11113628
    {'degree': 6, 'field': [-200, 0, 225, 0, -30, 0, 1], 'lmfdb_label': '259200.gp1', 'torsion': [2, 2]}
  • id: 11113629
    {'degree': 8, 'field': [-1850, 200, 2500, -1280, -40, -200, 4, -4, 1], 'lmfdb_label': '259200.gp1', 'torsion': [3]}
  • id: 11113630
    {'degree': 12, 'field': [10464, -20160, -48432, -33280, -12900, -5760, -4160, -960, -300, 0, -12, 0, 1], 'lmfdb_label': '259200.gp1', 'torsion': [4]}
• 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: 6424138
    {'conductor': 259200, 'conductor_valuation': 7, 'discriminant_valuation': 7, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '259200.gp1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6424139
    {'conductor': 259200, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '259200.gp1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6424140
    {'conductor': 259200, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '259200.gp1', 'prime': 5, 'reduction_type': 0, '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: 3306247
    {'adelic_gens': [[1, 0, 10, 1], [31, 10, 0, 1], [1, 10, 0, 1], [6, 5, 15, 36], [31, 12, 0, 7], [4, 9, 27, 1], [3, 16, 8, 3], [31, 10, 30, 11]], 'adelic_image': '40.10.0.?', 'conductor': 259200, 'lmfdb_label': '259200.gp1', 'prime': 0}
  • id: 930726
    {'conductor': 259200, 'elladic_image': '8.2.0.2', 'lmfdb_label': '259200.gp1', 'modell_image': '2G', 'prime': 2}
  • id: 930727
    {'conductor': 259200, 'elladic_image': '5.5.0.1', 'lmfdb_label': '259200.gp1', 'modell_image': '5S4', 'prime': 5}
• lmfdb_iso 259200.gp does not appear in ec_padic