Elliptic curve data - 55506.g1

Formats: - HTML - YAML - JSON - 2025-11-03T21:34:50.575293

• 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': '55506e', 'Clabel': '55506e1', 'Cnumber': 1, 'abc_quality': 1.0544733032417744, 'absD': 10656918606960704618496, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 696, 'ainvs': [1, 1, 0, -13782992, -20317686528], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 29], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 55506, 'degree': 4327680, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9977667145291591128933080733', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 6, 'isogeny_degrees': [1], 'jinv': [-11872994862835724607989, 436955947638718464], 'lmfdb_iso': '55506.g', 'lmfdb_label': '55506.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -13782992, -20317686528], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['696.2.0.?'], '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, 87], [3, 4, 18502], [5, 2, 18502], [11, 12, 5046], [23, 2, 27753], [29, 226, 66]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1559427570325406060974900652', 'prec': 100}, 'szpiro_ratio': 5.583185613352472, '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, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 0, 1, -1, 1, -3, -1, -5, 1], 'aplist': [-1, -1, 1, -1, -1, 0, -3, -5, -6, 0, 6, -3, -3, 5, -3, -10, 1, 10, -6, -8, -16, 2, 4, 6, 8], 'class_deg': 1, 'class_size': 1, 'conductor': 55506, 'isogeny_matrix': [[1]], 'lmfdb_iso': '55506.g', 'trace_hash': 233701596486498765}
• 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': '0.0024898484618349294457048344624', 'prec': 110}, 'conductor': 55506, 'gens': [], 'heights': [], 'lmfdb_label': '55506.g1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.039092755269118277101472926717', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.15637102107647310840589170686634257039', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [0, 0], '5': [4, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': 'a', '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '55506.g1'}
• ec_torsion_growth •

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

  
  
  • id: 2682344
    {'degree': 3, 'field': [6, -2, -1, 1], 'lmfdb_label': '55506.g1', 'torsion': [2]}
  • id: 2682345
    {'degree': 6, 'field': [696, 0, 49, 0, -14, 0, 1], 'lmfdb_label': '55506.g1', 'torsion': [2, 2]}
  • id: 2682346
    {'degree': 8, 'field': [658, -16225, -11918, -1451, -511, -143, 91, -4, 1], 'lmfdb_label': '55506.g1', 'torsion': [3]}
  • id: 2682347
    {'degree': 12, 'field': [-1854066, 2344052, -145941, -708612, 118877, 76096, -9745, -2520, -253, -32, 5, -4, 1], 'lmfdb_label': '55506.g1', '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: 1334331
    {'conductor': 55506, 'conductor_valuation': 1, 'discriminant_valuation': 23, 'j_denominator_valuation': 23, 'kodaira_symbol': 27, 'lmfdb_label': '55506.g1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1334332
    {'conductor': 55506, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '55506.g1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1334333
    {'conductor': 55506, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '55506.g1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1334334
    {'conductor': 55506, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '55506.g1', 'prime': 29, 'reduction_type': 0, '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

  
  {'adelic_gens': [[349, 2, 349, 3], [1, 0, 2, 1], [1, 2, 0, 1], [695, 2, 694, 3], [233, 2, 233, 3], [175, 2, 0, 1], [553, 2, 553, 3], [1, 1, 695, 0]], 'adelic_image': '696.2.0.?', 'conductor': 55506, 'lmfdb_label': '55506.g1', 'prime': 0}
• lmfdb_iso 55506.g does not appear in ec_padic