Elliptic curve data - 3648.o1

Formats: - HTML - YAML - JSON - 2023-03-31T22:32:12.209959

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '3648g', 'Clabel': '3648g3', 'Cnumber': 3, 'absD': 403439616, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, -1, 0, -6497, 203745], 'analytic_rank': 0, 'bad_primes': [2, 3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3648, 'degree': 3072, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.79471210863709187045641581232', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 4], 'jinv': [115714886617, 1539], 'lmfdb_iso': '3648.o', 'lmfdb_label': '3648.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -102, 385], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.24500866220282609366943236987', 'prec': 107}, '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, 2, 0, 0, 0, 1, 0, 0, 0, -6, 0, -2, 0, -6, 0, 1, 0], 'aplist': [0, -1, 2, 0, 0, -6, -6, 1, 4, -2, 8, 10, -2, 4, 12, 6, 12, 2, 4, 0, 10, 0, -16, -2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 3648, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '3648.o', 'trace_hash': 105683938187123035}
• 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': '0.20404306238858564706910178575', 'prec': 103}, 'conductor': 3648, 'gens': [], 'heights': [], 'lmfdb_label': '3648.o1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.5348491927152808704657754926', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5348491927152808704657754925785347432', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[47, 0, 1]], 'xcoord_integral_points': [47]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '3648.o1'}
• ec_torsion_growth •

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

  
  
  • id: 190323
    {'degree': 2, 'field': [-38, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [4]}
  • id: 190322
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [2, 2]}
  • id: 190324
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [4]}
  • id: 190325
    {'degree': 4, 'field': [81, 0, -20, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [2, 4]}
  • id: 190329
    {'degree': 8, 'field': [-48, 0, 88, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [6]}
  • id: 190328
    {'degree': 8, 'field': [9, 0, 30, 0, 31, 0, 8, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [8]}
  • id: 190327
    {'degree': 8, 'field': [16, 0, -120, 0, 176, 0, -30, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [8]}
  • id: 190326
    {'degree': 8, 'field': [225, 0, 488, 0, -14, 0, 8, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [2, 4]}
  • id: 190332
    {'degree': 16, 'field': [4, 144, -1912, -8544, 17252, 14016, -28236, -6672, 17765, 780, -5100, 72, 713, -12, -46, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [2, 8]}
  • id: 190331
    {'degree': 16, 'field': [81, 0, 1692, 0, 35074, 0, 5856, 0, 3147, 0, -736, 0, 114, 0, -12, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [2, 8]}
  • id: 190335
    {'degree': 16, 'field': [121, 0, 698, 0, 2197, 0, -6468, 0, 2538, 0, -474, 0, 100, 0, -16, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [12]}
  • id: 190334
    {'degree': 16, 'field': [3249, 0, -10944, 0, 48888, 0, -47504, 0, 5390, 0, -1844, 0, -47, 0, -28, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [12]}
  • id: 190330
    {'degree': 16, 'field': [3969, -8316, 8712, -9348, 7366, -2520, 120, 1060, -1625, 920, -280, 20, 94, -76, 32, -8, 1], 'lmfdb_label': '3648.o1', 'torsion': [4, 4]}
  • id: 190333
    {'degree': 16, 'field': [251001, 0, -815532, 0, -806039, 0, -210468, 0, -7062, 0, 2468, 0, 24, 0, 0, 0, 1], 'lmfdb_label': '3648.o1', 'torsion': [2, 6]}
• 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: 67163
    {'conductor': 3648, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '3648.o1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 67164
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '3648.o1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 67165
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3648.o1', 'prime': 19, '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

  
  
  • id: 1687697
    {'adelic_gens': [[449, 8, 448, 9], [388, 1, 407, 6], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 450, 451], [288, 65, 313, 360], [53, 54, 158, 389], [305, 8, 308, 33]], 'adelic_image': '456.48.0.?', 'conductor': 3648, 'lmfdb_label': '3648.o1', 'prime': 0}
  • id: 18277
    {'conductor': 3648, 'elladic_image': '8.12.0.8', 'lmfdb_label': '3648.o1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3648.o does not appear in ec_padic