Elliptic curve data - 412224.b2

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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
  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[]

  
  {'Ciso': '412224b', 'Clabel': '412224b2', 'Cnumber': 2, 'abc_quality': 1.0060248717974618, 'absD': 98289383681517165622591488, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 456, 'ainvs': [0, -1, 0, 99082015, 288785548161], 'analytic_rank': 0, 'bad_primes': [2, 3, 19, 113], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 412224, 'degree': 242810880, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6748022256768453524838752215', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [410363075617640914325831, 374944243169850027552], 'lmfdb_iso': '412224.b', 'lmfdb_label': '412224.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 1548157, -563453715], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '228.6.0.?', '456.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1], [3, 4, 137408], [13, 2, 137408], [19, 20, 21696], [113, 114, 3648]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.6350814548369273883580270393', 'prec': 100}, 'szpiro_ratio': 5.170261645785413, '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, -1, 0, -4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 4, 0, -6, 0, 1, 0], 'aplist': [0, -1, -4, 4, 0, 0, -6, 1, -6, 6, -10, 12, 10, -4, 6, -2, -12, -6, -8, 0, -10, -10, 12, 6, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 412224, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '412224.b', 'trace_hash': 1145820694238199992}
• 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': '0.00064284658717004650288911604388', 'prec': 113}, 'conductor': 412224, 'gens': [], 'heights': [], 'lmfdb_label': '412224.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.039147907850851019953655496107', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.31318326280680815962924396885273214386', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-2713, 0, 1]], 'xcoord_integral_points': [-2713]}
• lmfdb_label 412224.b2 does not appear in ec_iwasawa
• lmfdb_label 412224.b2 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: 10187723
    {'conductor': 412224, 'conductor_valuation': 6, 'discriminant_valuation': 23, 'j_denominator_valuation': 5, 'kodaira_symbol': -17, 'lmfdb_label': '412224.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 10187724
    {'conductor': 412224, 'conductor_valuation': 1, 'discriminant_valuation': 26, 'j_denominator_valuation': 26, 'kodaira_symbol': 30, 'lmfdb_label': '412224.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 10187725
    {'conductor': 412224, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '412224.b2', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 10187726
    {'conductor': 412224, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '412224.b2', 'prime': 113, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 4214957
    {'adelic_gens': [[1, 2, 2, 5], [305, 4, 154, 9], [1, 4, 0, 1], [97, 4, 194, 9], [172, 289, 57, 400], [453, 4, 452, 5], [2, 1, 227, 0], [1, 0, 4, 1], [3, 4, 8, 11]], 'adelic_image': '456.12.0.?', 'conductor': 412224, 'lmfdb_label': '412224.b2', 'prime': 0}
  • id: 1394883
    {'conductor': 412224, 'elladic_image': '8.6.0.5', 'lmfdb_label': '412224.b2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 412224.b does not appear in ec_padic