Elliptic curve isogeny class data - 49.a

Formats: - HTML - YAML - JSON - 2025-04-29T14:03:47.747704

• 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, 0, 0, 0, -3, -3, 0, 4, 0, 0, 0, 0, -1, 0, -3, 0, 0], 'aplist': [1, 0, 0, 0, 4, 0, 0, 0, 8, 2, 0, -6, 0, -12, 0, -10, 0, 0, 4, 16, 0, 8, 0, 0, 0], 'class_deg': 14, 'class_size': 4, 'conductor': 49, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '49.a', 'trace_hash': 1094831497817794886}
• lmfdb_iso 49.a does not appear in ec_padic
• 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[]

  
  
  • id: 121
    {'Ciso': '49a', 'Clabel': '49a4', 'Cnumber': 4, 'abc_quality': 1.1980441775334598, 'absD': 40353607, 'ainvs': [1, -1, 0, -1822, 30393], 'analytic_rank': 0, 'bad_primes': [7], 'class_deg': 14, 'class_size': 4, 'cm': -28, 'conductor': 49, 'degree': 14, 'elladic_images': ['7.48.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.52039027575200689013698072272', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 14, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [16581375, 1], 'lmfdb_iso': '49.a', 'lmfdb_label': '49.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -37, -78], 'min_quad_twist_disc': -7, 'modell_images': ['7B.1.2'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 1, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[7, 20, 1]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.93904233603947808869203383486', 'prec': 107}, 'szpiro_ratio': 8.771469225736265, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 120
    {'Ciso': '49a', 'Clabel': '49a3', 'Cnumber': 3, 'abc_quality': 0.9802957926219806, 'absD': 40353607, 'ainvs': [1, -1, 0, -107, 552], 'analytic_rank': 0, 'bad_primes': [7], 'class_deg': 14, 'class_size': 4, 'cm': -7, 'conductor': 49, 'degree': 7, 'elladic_images': ['7.48.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.17381668547203423542836466200', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 7, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [-3375, 1], 'lmfdb_iso': '49.a', 'lmfdb_label': '49.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -2, -1], 'min_quad_twist_disc': -7, 'modell_images': ['7B.1.2'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 1, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[7, 20, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2856159263194507434006498956', 'prec': 103}, 'szpiro_ratio': 6.693725102160739, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 119
    {'Ciso': '49a', 'Clabel': '49a2', 'Cnumber': 2, 'abc_quality': 1.1980441775334598, 'absD': 343, 'ainvs': [1, -1, 0, -37, -78], 'analytic_rank': 0, 'bad_primes': [7], 'class_deg': 14, 'class_size': 4, 'cm': -28, 'conductor': 49, 'degree': 2, 'elladic_images': ['7.48.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.45256479877564976241569564900', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [16581375, 1], 'lmfdb_iso': '49.a', 'lmfdb_label': '49.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -37, -78], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.5'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 1, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[7, 20, 1]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.93904233603947808869203383486', 'prec': 107}, 'szpiro_ratio': 5.771469225736265, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 118
    {'Ciso': '49a', 'Clabel': '49a1', 'Cnumber': 1, 'abc_quality': 0.9802957926219806, 'absD': 343, 'ainvs': [1, -1, 0, -2, -1], 'analytic_rank': 0, 'bad_primes': [7], 'class_deg': 14, 'class_size': 4, 'cm': -7, 'conductor': 49, 'degree': 1, 'elladic_images': ['7.48.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.79913838905562241712431170973', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [-3375, 1], 'lmfdb_iso': '49.a', 'lmfdb_label': '49.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -2, -1], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.5'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 1, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[7, 20, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2856159263194507434006498956', 'prec': 103}, 'szpiro_ratio': 3.6937251021607387, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}