Elliptic curve data - 48050.o1

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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': '48050r', 'Clabel': '48050r1', 'Cnumber': 1, 'abc_quality': 0.8809241450872604, 'absD': 72150078125000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 8, 'ainvs': [1, 0, 0, -12513, 350017], 'analytic_rank': 0, 'bad_primes': [2, 5, 31], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 48050, 'degree': 129600, 'elladic_images': ['8.2.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3618143202552913554075367903', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1], 'jinv': [24025, 8], 'lmfdb_iso': '48050.o', 'lmfdb_label': '48050.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -500, 2600], 'min_quad_twist_disc': 5, 'modell_images': [], 'modm_images': ['8.2.0.b.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 24025], [3, 2, 24025], [5, 2, 1922], [31, 332, 50]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1240463416015077054028174289', 'prec': 103}, 'szpiro_ratio': 3.7028931122751665, '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, 1, -2, 1, 0, -2, -3, 1, 1, 0, 2, -2, 0, -3, 0, 1, -2, 1, 2, 0], 'aplist': [1, -2, 0, -3, 2, 0, -2, 2, 1, 2, 0, -4, 6, 4, -3, -8, 8, 6, 2, 9, -3, 11, 0, 6, -1], 'class_deg': 1, 'class_size': 1, 'conductor': 48050, 'isogeny_matrix': [[1]], 'lmfdb_iso': '48050.o', 'trace_hash': 107795717374707890}
• 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': '0.065636151787275087353821055143', 'prec': 107}, 'conductor': 48050, 'gens': [], 'heights': [], 'lmfdb_label': '48050.o1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.56646989127871873827859341807', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6994096738361562148357802541965658415', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [2, 0], '5': 'a', '7': [0, 0], '11': [0, 0], '13': [0, 0, 0], '17': [0, 0], '19': [0, 0], '23': [2, 0], '29': [0, 0], '31': 'a', '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '48050.o1'}
• ec_torsion_growth •

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

  
  
  • id: 2342259
    {'degree': 3, 'field': [-333, -103, -1, 1], 'lmfdb_label': '48050.o1', 'torsion': [2]}
  • id: 2342260
    {'degree': 6, 'field': [-23762, 0, 3037, 0, -104, 0, 1], 'lmfdb_label': '48050.o1', 'torsion': [2, 2]}
  • id: 2342261
    {'degree': 8, 'field': [-570, 915, -909, 634, -310, 100, -20, -1, 1], 'lmfdb_label': '48050.o1', 'torsion': [3]}
  • id: 2342262
    {'degree': 12, 'field': [1024, 22528, -19968, 179840, -168440, 105088, -38914, 9494, -1355, 40, 12, -6, 1], 'lmfdb_label': '48050.o1', '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: 1148356
    {'conductor': 48050, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '48050.o1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1148357
    {'conductor': 48050, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '48050.o1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1148358
    {'conductor': 48050, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '48050.o1', 'prime': 31, '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: 1984227
    {'adelic_gens': [[7, 2, 0, 1], [1, 0, 2, 1], [1, 1, 7, 0], [1, 2, 0, 1], [5, 2, 5, 3], [7, 2, 6, 3]], 'adelic_image': '8.2.0.?', 'conductor': 48050, 'lmfdb_label': '48050.o1', 'prime': 0}
  • id: 207417
    {'conductor': 48050, 'elladic_image': '8.2.0.2', 'lmfdb_label': '48050.o1', 'modell_image': '2G', 'prime': 2}
• lmfdb_iso 48050.o does not appear in ec_padic