Elliptic curve data - 405720.gr4

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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': '405720gr', 'Clabel': '405720gr5', 'Cnumber': 5, 'abc_quality': 0.9963375475867037, 'absD': 21664514799210818307225600, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 38640, 'ainvs': [0, 0, 0, -11501427, -224443174354], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 405720, 'degree': 88080384, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5409165410149669750776337788', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 173, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-957928673903042, 123339801817575], 'lmfdb_iso': '405720.gr', 'lmfdb_label': '405720.gr4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -26080, -24244000], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '24.24.0-8.n.1.2', '40.24.0.ca.2', '56.24.0.bl.1', '84.12.0.?', '120.48.0.?', '168.48.0.?', '280.48.0.?', '368.24.0.?', '840.96.0.?', '1104.48.0.?', '1840.48.0.?', '2576.48.0.?', '5520.96.0.?', '7728.96.0.?', '12880.96.1.?', '38640.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.809257704667457325084706725', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3832704066399722765282053439', 'prec': 100}, 'szpiro_ratio': 5.095236562508013, '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, 1, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, 1, 0, 4, 2, 2, 4, 1, 2, -8, 6, -6, -4, 8, 10, -12, -14, -12, -16, 14, 8, -12, -14, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 405720, 'isogeny_matrix': [[1, 8, 2, 4, 4, 8], [8, 1, 4, 8, 2, 4], [2, 4, 1, 2, 2, 4], [4, 8, 2, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '405720.gr', 'trace_hash': 934877742675962533}
• 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': '0.00084023152254196396774039296358', 'prec': 113}, 'conductor': 405720, 'gens': [[31430242, 175952065400, 21]], 'heights': [{'__RealLiteral__': 0, 'data': '11.809257704667457325084706725', 'prec': 100}], 'lmfdb_label': '405720.gr4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.030168434141462191352955962963', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.400538026330084845237500284089900553', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[6706, 0, 1]], 'xcoord_integral_points': [6706]}
• lmfdb_label 405720.gr4 does not appear in ec_iwasawa
• lmfdb_label 405720.gr4 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: 10032821
    {'conductor': 405720, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '405720.gr4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 10032822
    {'conductor': 405720, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '405720.gr4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 10032823
    {'conductor': 405720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '405720.gr4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 10032824
    {'conductor': 405720, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '405720.gr4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 10032825
    {'conductor': 405720, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '405720.gr4', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 4177971
    {'adelic_gens': [[15, 2, 38542, 38627], [6721, 25776, 28008, 13009], [1, 16, 0, 1], [16108, 3225, 19323, 6442], [33811, 25776, 37038, 3349], [7741, 25776, 35808, 12565], [25759, 0, 0, 38639], [1, 0, 16, 1], [38625, 16, 38624, 17], [29432, 12879, 7281, 38630], [5, 4, 38636, 38637]], 'adelic_image': '38640.192.1.?', 'conductor': 405720, 'lmfdb_label': '405720.gr4', 'prime': 0}
  • id: 1376307
    {'conductor': 405720, 'elladic_image': '8.12.0.5', 'lmfdb_label': '405720.gr4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 405720.gr does not appear in ec_padic