Elliptic curve data - 3648.bc1

Formats: - HTML - YAML - JSON - 2024-05-23T15:12:45.382993

• 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': '3648bh', 'Clabel': '3648bh3', 'Cnumber': 3, 'abc_quality': 1.0077462703550282, 'absD': 21576548352, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 456, 'ainvs': [0, 1, 0, -27393, 1735935], 'analytic_rank': 0, 'bad_primes': [2, 3, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 3648, 'degree': 6912, 'elladic_images': ['8.6.0.4', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1452228167900207152511757515', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [8671983378625, 82308], 'lmfdb_iso': '3648.bc', 'lmfdb_label': '3648.bc1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -428, -3444], 'min_quad_twist_disc': -8, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.d.1', '12.24.0-6.a.1.5', '24.48.0-24.bx.1.9', '114.24.0.?', '228.48.0.?', '456.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, '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': '0.10550204595010275112532756931', 'prec': 103}, 'szpiro_ratio': 5.153390174096828, '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, 0, 0, 4, 0, 1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 1, 0], 'aplist': [0, 1, 0, 4, 0, 4, 6, 1, 6, -6, -2, 4, 6, -4, -6, -6, -12, -14, 8, 0, 14, 10, -12, -6, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 3648, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '3648.bc', 'trace_hash': 438368526606129504}
• 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': '0.10122134417167311070492904143', 'prec': 103}, 'conductor': 3648, 'gens': [], 'heights': [], 'lmfdb_label': '3648.bc1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0910471272104013438578831419', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2731413816312040315736494256146157083', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[95, 0, 1]], 'xcoord_integral_points': [95]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [5, 0], '19': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '3648.bc1'}
• ec_torsion_growth •

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

  
  
  • id: 190870
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '3648.bc1', 'torsion': [2, 2]}
  • id: 190871
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '3648.bc1', 'torsion': [6]}
  • id: 190872
    {'degree': 4, 'field': [6, 0, -1, -2, 1], 'lmfdb_label': '3648.bc1', 'torsion': [4]}
  • id: 190873
    {'degree': 4, 'field': [64, 0, -22, 0, 1], 'lmfdb_label': '3648.bc1', 'torsion': [2, 6]}
  • id: 190874
    {'degree': 6, 'field': [18, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3648.bc1', 'torsion': [6]}
  • id: 190875
    {'degree': 8, 'field': [-912, 0, 3648, 2280, 538, 28, -27, -2, 1], 'lmfdb_label': '3648.bc1', 'torsion': [2, 4]}
  • id: 190877
    {'degree': 8, 'field': [9, 6, 7, 10, 2, -2, 5, -2, 1], 'lmfdb_label': '3648.bc1', 'torsion': [12]}
  • id: 190876
    {'degree': 8, 'field': [256, 0, 360, 0, 41, 0, -6, 0, 1], 'lmfdb_label': '3648.bc1', 'torsion': [2, 4]}
  • id: 190880
    {'degree': 12, 'field': [342, -2052, 5022, -5736, 2052, 1260, -733, 138, -27, 4, 9, -6, 1], 'lmfdb_label': '3648.bc1', 'torsion': [12]}
  • id: 190878
    {'degree': 12, 'field': [361, -114, -249, 670, -180, -234, 177, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '3648.bc1', 'torsion': [3, 6]}
  • id: 190879
    {'degree': 12, 'field': [666976, -820800, 5232, 149760, 94920, 4320, 6724, 0, 60, -180, 12, 0, 1], 'lmfdb_label': '3648.bc1', 'torsion': [2, 6]}
  • id: 190883
    {'degree': 16, 'field': [121, -550, 1411, -3058, 4973, -4000, 1542, 548, -634, 52, 270, -128, -19, 34, -5, -2, 1], 'lmfdb_label': '3648.bc1', 'torsion': [2, 12]}
  • id: 190881
    {'degree': 16, 'field': [20736, 41472, 44928, 8064, -21264, -21504, 576, 9120, 3934, -2048, -1080, 120, 199, -12, -6, -4, 1], 'lmfdb_label': '3648.bc1', 'torsion': [8]}
  • id: 190882
    {'degree': 16, 'field': [209764, 0, 279180, 0, 39169, 0, -40326, 0, -4932, 0, -3168, 0, 1192, 0, -66, 0, 1], 'lmfdb_label': '3648.bc1', 'torsion': [2, 12]}
  • id: 190884
    {'degree': 18, 'field': [-732880224, 0, 604953360, 0, -196285680, 0, 37449972, 0, -5020056, 0, 503712, 0, -40002, 0, 1872, 0, -48, 0, 1], 'lmfdb_label': '3648.bc1', 'torsion': [18]}
• 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: 67343
    {'conductor': 3648, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '3648.bc1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 67344
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3648.bc1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 67345
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '3648.bc1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1687651
    {'adelic_gens': [[129, 206, 226, 307], [11, 2, 406, 447], [1, 0, 12, 1], [1, 6, 6, 37], [227, 444, 450, 383], [1, 12, 0, 1], [445, 12, 444, 13], [86, 3, 277, 448], [58, 3, 117, 448]], 'adelic_image': '456.96.1.?', 'conductor': 3648, 'lmfdb_label': '3648.bc1', 'prime': 0}
  • id: 18231
    {'conductor': 3648, 'elladic_image': '8.6.0.4', 'lmfdb_label': '3648.bc1', 'modell_image': '2B', 'prime': 2}
  • id: 18232
    {'conductor': 3648, 'elladic_image': '3.4.0.1', 'lmfdb_label': '3648.bc1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 3648.bc does not appear in ec_padic