Elliptic curve data - 54096.bm1

Formats: - HTML - YAML - JSON - 2025-10-29T11:27:50.510742

• 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': '54096g', 'Clabel': '54096g1', 'Cnumber': 1, 'abc_quality': 0.8800308023065714, 'absD': 461898361903104, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 3864, 'ainvs': [0, -1, 0, -19224, -1450224], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 23], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 54096, 'degree': 230400, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5164227423939312808365339783', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 38, 'isogeny_degrees': [1], 'jinv': [-3261064466, 1917027], 'lmfdb_iso': '54096.bm', 'lmfdb_label': '54096.bm1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -392, -4116], 'min_quad_twist_disc': 28, 'modell_images': [], 'modm_images': ['3864.2.0.?'], '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, 3381], [3, 4, 18032], [5, 2, 18032], [7, 32, 1104], [23, 24, 2352]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.091917247647008572015271838093', 'prec': 110}, 'szpiro_ratio': 3.8451494152917887, '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, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, -3, 0, 4, 0, 0, 0], 'aplist': [0, -1, 3, 0, 0, 1, 4, 0, -1, 5, -10, -3, 11, 9, -3, 12, 10, 10, 12, -6, 4, -12, 12, -6, -9], 'class_deg': 1, 'class_size': 1, 'conductor': 54096, 'isogeny_matrix': [[1]], 'lmfdb_iso': '54096.bm', 'trace_hash': 1475936640700824660}
• 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': '0.048178352128004957056192690761', 'prec': 107}, 'conductor': 54096, 'gens': [], 'heights': [], 'lmfdb_label': '54096.bm1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.19739613570986586230465696391', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1583381713578537968745114225318332509', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '7': 'a', '11': [0, 0, 0], '13': [2, 0], '17': [0, 0], '19': [0, 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': '54096.bm1'}
• ec_torsion_growth •

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

  
  
  • id: 2615012
    {'degree': 3, 'field': [24, 0, -1, 1], 'lmfdb_label': '54096.bm1', 'torsion': [2]}
  • id: 2615013
    {'degree': 6, 'field': [7056, 2016, 942, 144, 25, -2, 1], 'lmfdb_label': '54096.bm1', 'torsion': [2, 2]}
  • id: 2615014
    {'degree': 8, 'field': [-1217307, 0, -101528, 0, -3822, 0, 0, 0, 1], 'lmfdb_label': '54096.bm1', 'torsion': [3]}
  • id: 2615015
    {'degree': 12, 'field': [-15456, -15528, -3886, -15960, -2607, 72, 1324, 360, 2, -144, -6, 0, 1], 'lmfdb_label': '54096.bm1', '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: 1297882
    {'conductor': 54096, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '54096.bm1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1297883
    {'conductor': 54096, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '54096.bm1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1297884
    {'conductor': 54096, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '54096.bm1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1297885
    {'conductor': 54096, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '54096.bm1', 'prime': 23, 'reduction_type': -1, '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': [[1, 0, 2, 1], [1, 2, 0, 1], [2761, 2, 2761, 3], [1933, 2, 1933, 3], [3863, 2, 3862, 3], [1289, 2, 1289, 3], [1, 1, 3863, 0], [967, 2, 0, 1], [2857, 2, 2857, 3]], 'adelic_image': '3864.2.0.?', 'conductor': 54096, 'lmfdb_label': '54096.bm1', 'prime': 0}
• lmfdb_iso 54096.bm does not appear in ec_padic