Elliptic curve data - 48552.z1

Formats: - HTML - YAML - JSON - 2025-09-22T21:16:59.988949

• 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': '48552u', 'Clabel': '48552u1', 'Cnumber': 1, 'abc_quality': 0.9874175650711245, 'absD': 90402144657368967714816, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 24, 'ainvs': [0, 1, 0, -17911160, 32559875952], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 48552, 'degree': 4328064, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1358332899010578514849758572', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1], 'jinv': [-44480898716402, 6327867987], 'lmfdb_iso': '48552.z', 'lmfdb_label': '48552.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -61976, 6649164], 'min_quad_twist_disc': 17, 'modell_images': [], 'modm_images': ['24.2.0.b.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 867], [3, 4, 16184], [7, 8, 6936], [17, 114, 56]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.61163947835029726435282333395', 'prec': 103}, 'szpiro_ratio': 5.739940960590745, '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, 1, 0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 6, 0], 'aplist': [0, 1, 1, 1, -1, 0, 0, 6, 6, -7, -3, -6, 2, 4, -6, -11, 5, 8, 4, -6, -13, 17, 12, 0, 17], 'class_deg': 1, 'class_size': 1, 'conductor': 48552, 'isogeny_matrix': [[1]], 'lmfdb_iso': '48552.z', 'trace_hash': 1571074246537680172}
• 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': '0.0018890776596342741733886916828', 'prec': 110}, 'conductor': 48552, 'gens': [], 'heights': [], 'lmfdb_label': '48552.z1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10377753406657641392185409129', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5284361582635980733430391039022327585', 'prec': 130}, 'tamagawa_product': 34, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [2, 0], '7': [1, 0], '11': [0, 0], '13': [0, 0, 0], '17': 'a', '19': [0, 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': '48552.z1'}
• ec_torsion_growth •

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

  
  
  • id: 2364375
    {'degree': 3, 'field': [39, -11, -1, 1], 'lmfdb_label': '48552.z1', 'torsion': [2]}
  • id: 2364376
    {'degree': 6, 'field': [24, -120, 142, 52, 15, -2, 1], 'lmfdb_label': '48552.z1', 'torsion': [2, 2]}
  • id: 2364377
    {'degree': 8, 'field': [-3, 0, -76, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '48552.z1', 'torsion': [3]}
  • id: 2364378
    {'degree': 12, 'field': [-166146, -420342, -367509, -295332, -110923, -49276, -5594, -2888, 400, -118, 35, -4, 1], 'lmfdb_label': '48552.z1', '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: 1160305
    {'conductor': 48552, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '48552.z1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1160306
    {'conductor': 48552, 'conductor_valuation': 1, 'discriminant_valuation': 17, 'j_denominator_valuation': 17, 'kodaira_symbol': 21, 'lmfdb_label': '48552.z1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 17}
  • id: 1160307
    {'conductor': 48552, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '48552.z1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1160308
    {'conductor': 48552, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '48552.z1', 'prime': 17, '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

  
  {'adelic_gens': [[7, 2, 0, 1], [1, 2, 0, 1], [17, 2, 17, 3], [1, 0, 2, 1], [23, 2, 22, 3], [13, 2, 13, 3], [1, 1, 23, 0]], 'adelic_image': '24.2.0.?', 'conductor': 48552, 'lmfdb_label': '48552.z1', 'prime': 0}
• lmfdb_iso 48552.z does not appear in ec_padic