Elliptic curve data - 3648.n4

Formats: - HTML - YAML - JSON - 2024-06-02T02:02:27.798464

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '3648h', 'Clabel': '3648h1', 'Cnumber': 1, 'abc_quality': 0.9683473674013149, 'absD': 7978176, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 152, 'ainvs': [0, -1, 0, -52, 70], 'analytic_rank': 0, 'bad_primes': [2, 3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3648, 'degree': 768, 'elladic_images': ['8.24.0.104'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.017016770977627810395444526422', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 4], 'jinv': [247673152, 124659], 'lmfdb_iso': '3648.n', 'lmfdb_label': '3648.n4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -209, -351], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.m.1.7', '76.12.0.?', '152.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.32955681930234484431317153431', 'prec': 107}, 'szpiro_ratio': 2.8635322567955663, '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, -4, 0, 1, 0, -4, 0, -2, 0, -2, 0, 2, 0, 1, 0], 'aplist': [0, -1, 2, -4, -4, -2, 2, 1, -4, 6, 0, -2, -6, 12, -4, -2, 12, 10, 4, 0, 10, -8, 12, -14, 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.n', 'trace_hash': 140765390628873711}
• 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': '0.96653908448306746621659361296', 'prec': 103}, 'conductor': 3648, 'gens': [], 'heights': [], 'lmfdb_label': '3648.n4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.0661816643192702468786432000', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0330908321596351234393215999796468010', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[7, 0, 1]], 'xcoord_integral_points': [7]}
• 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.n4'}
• ec_torsion_growth •

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

  
  
  • id: 190351
    {'degree': 2, 'field': [-38, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [4]}
  • id: 190350
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [2, 2]}
  • id: 190352
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [4]}
  • id: 190354
    {'degree': 4, 'field': [19, 0, -38, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [8]}
  • id: 190353
    {'degree': 4, 'field': [81, 0, -20, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [2, 4]}
  • id: 190358
    {'degree': 8, 'field': [-972, 0, 1224, 0, 108, 0, 0, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [6]}
  • id: 190357
    {'degree': 8, 'field': [17, 500, -1604, -660, 756, 132, -52, -4, 1], 'lmfdb_label': '3648.n4', 'torsion': [2, 8]}
  • id: 190355
    {'degree': 8, 'field': [225, 0, 488, 0, -14, 0, 8, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [2, 4]}
  • id: 190356
    {'degree': 8, 'field': [361, 0, 0, 0, -34, 0, 0, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [8]}
  • id: 190361
    {'degree': 16, 'field': [-2243862, 0, 73798128, -147596256, 65155104, 17950896, -9320184, -738720, 795132, 8352, -48384, -4464, 412, 400, -48, -8, 1], 'lmfdb_label': '3648.n4', 'torsion': [16]}
  • id: 190364
    {'degree': 16, 'field': [324, 0, -1296, 0, 1296, 0, -392, 0, 500, 0, 64, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [12]}
  • id: 190360
    {'degree': 16, 'field': [657, 972, -392, -804, -716, 952, 592, -1212, 1077, -1016, 852, -524, 258, -108, 36, -8, 1], 'lmfdb_label': '3648.n4', 'torsion': [2, 8]}
  • id: 190359
    {'degree': 16, 'field': [3969, -8316, 8712, -9348, 7366, -2520, 120, 1060, -1625, 920, -280, 20, 94, -76, 32, -8, 1], 'lmfdb_label': '3648.n4', 'torsion': [4, 4]}
  • id: 190362
    {'degree': 16, 'field': [31329, 0, 63228, 0, 2338600, 0, 1553244, 0, -25170, 0, -16348, 0, -264, 0, 36, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [2, 6]}
  • id: 190363
    {'degree': 16, 'field': [69906321, 0, -48528396, 0, 20111004, 0, -4498988, 0, 583898, 0, -47996, 0, 2524, 0, -76, 0, 1], 'lmfdb_label': '3648.n4', 'torsion': [12]}
• 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: 67169
    {'conductor': 3648, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '3648.n4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 67170
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '3648.n4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 67171
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3648.n4', '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: 1687696
    {'adelic_gens': [[145, 8, 144, 9], [1, 0, 8, 1], [1, 8, 0, 1], [7, 6, 146, 147], [125, 130, 14, 93], [84, 1, 103, 6], [56, 125, 133, 132], [1, 4, 4, 17]], 'adelic_image': '152.48.0.?', 'conductor': 3648, 'lmfdb_label': '3648.n4', 'prime': 0}
  • id: 18276
    {'conductor': 3648, 'elladic_image': '8.24.0.104', 'lmfdb_label': '3648.n4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3648.n does not appear in ec_padic