Elliptic curve data - 78400.hm1

Formats: - HTML - YAML - JSON - 2024-04-27T15:18:50.155188

• 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': '78400bf', 'Clabel': '78400bf1', 'Cnumber': 1, 'abc_quality': 0.8374478418484275, 'absD': 4519603984000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 280, 'ainvs': [0, 1, 0, -80033, -8118937], 'analytic_rank': 0, 'bad_primes': [2, 5, 7], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 78400, 'degree': 376320, 'elladic_images': ['2.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7473740733906189860309647947', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 194, 'isogeny_degrees': [1], 'jinv': [12544, 1], 'lmfdb_iso': '78400.hm', 'lmfdb_label': '78400.hm1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -16, 29], 'min_quad_twist_disc': -280, 'modell_images': ['2Cn'], 'modm_images': ['2.2.0.a.1', '14.6.0.a.1', '280.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2565593241724800467049022593', 'prec': 103}, 'szpiro_ratio': 4.036015691496724, '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, 1, 0, 0, 0, 0, 0, -2, 0, -3, 0, 6, 0, 0, 0, -5, 0, 1, 0], 'aplist': [0, 1, 0, 0, -3, 6, -5, 1, 7, -2, 5, 3, 2, -4, 5, -1, 15, -5, -9, 0, 7, 1, -12, -7, -2], 'class_deg': 1, 'class_size': 1, 'conductor': 78400, 'isogeny_matrix': [[1]], 'lmfdb_iso': '78400.hm', 'trace_hash': 1715439883360694591}
• 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': '0.030356392829193396715774575319', 'prec': 107}, 'conductor': 78400, 'gens': [], 'heights': [], 'lmfdb_label': '78400.hm1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.28528090368693659879061708994', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5675281331824293891155538094984839382', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': 'a', '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [2, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '78400.hm1'}
• ec_torsion_growth •

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

  
  
  • id: 3700073
    {'degree': 3, 'field': [1, -2, -1, 1], 'lmfdb_label': '78400.hm1', 'torsion': [2, 2]}
  • id: 3700074
    {'degree': 8, 'field': [-91875, 0, 50750, 0, -1050, 0, 0, 0, 1], 'lmfdb_label': '78400.hm1', 'torsion': [3]}
  • id: 3700075
    {'degree': 12, 'field': [765625, 0, 0, 0, -91875, 0, 8750, 0, -350, 0, 0, 0, 1], 'lmfdb_label': '78400.hm1', 'torsion': [2, 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: 1907973
    {'conductor': 78400, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '78400.hm1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1907974
    {'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '78400.hm1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1907975
    {'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '78400.hm1', 'prime': 7, '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: 2181789
    {'adelic_gens': [[1, 2, 2, 5], [1, 4, 0, 1], [199, 220, 200, 219], [191, 225, 235, 56], [139, 0, 0, 279], [277, 4, 276, 5], [1, 0, 4, 1], [71, 60, 70, 1], [109, 110, 260, 89], [223, 0, 0, 279], [3, 2, 272, 275]], 'adelic_image': '280.12.0.?', 'conductor': 78400, 'lmfdb_label': '78400.hm1', 'prime': 0}
  • id: 323341
    {'conductor': 78400, 'elladic_image': '2.2.0.1', 'lmfdb_label': '78400.hm1', 'modell_image': '2Cn', 'prime': 2}
• lmfdb_iso 78400.hm does not appear in ec_padic