Elliptic curve data - 159120.b1

Formats: - HTML - YAML - JSON - 2026-06-18T02:57:22.997220

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '159120bd', 'Clabel': '159120bd3', 'Cnumber': 3, 'abc_quality': 0.9734129542300942, 'absD': 292446181498165493760, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -11033283, 14082028738], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 159120, 'degree': 8847360, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8151488846296302804816651877', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [49745123032831462081, 97939634471640], 'lmfdb_iso': '159120.b', 'lmfdb_label': '159120.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -76620, 8117397], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.3', '40.12.0.bb.1', '52.12.0-4.c.1.2', '120.24.0.?', '312.24.0.?', '520.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.56717112090193150297859786514', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 585], [3, 6, 17680], [5, 6, 31824], [13, 14, 12240], [17, 18, 9360]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5726955597356301253668104478', 'prec': 100}, 'szpiro_ratio': 5.0313769263551675, '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, 0, 0, -1, 0, -4, 0, 0, 0, -4, 0, 1, 0, 0, 0, 1, 0, -8, 0], 'aplist': [0, 0, -1, -4, -4, 1, 1, -8, -4, -2, 0, 6, 6, -4, 0, 2, -4, 6, -12, 0, 6, 0, 12, -10, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 159120, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '159120.b', 'trace_hash': 1421017662801374014}
• 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': '0.0035875069189924010780706935913', 'prec': 110}, 'conductor': 159120, 'gens': [[2033, 7344, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.56717112090193150297859786514', 'prec': 103}], 'lmfdb_label': '159120.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.17321201195356155529085878597', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1437072311481684985113899625590187917', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[1982, 0, 1]], 'xcoord_integral_points': [1982, 2033, 2271, 4583, 16721]}
• lmfdb_label 159120.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7120248
    {'degree': 2, 'field': [-390, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [2, 2]}
  • id: 7120249
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [4]}
  • id: 7120250
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '159120.b1', 'torsion': [4]}
  • id: 7120251
    {'degree': 4, 'field': [699, 66, -65, -2, 1], 'lmfdb_label': '159120.b1', 'torsion': [2, 4]}
  • id: 7120255
    {'degree': 8, 'field': [-432, 0, -600, 0, 273, 0, -33, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [6]}
  • id: 7120253
    {'degree': 8, 'field': [4225, 0, -61100, 0, 5580, 0, -140, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [8]}
  • id: 7120252
    {'degree': 8, 'field': [1934881, 0, 252148, 0, -2106, 0, 52, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [2, 4]}
  • id: 7120254
    {'degree': 8, 'field': [2433600, 0, 60840, 0, -39, 0, 39, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [8]}
  • id: 7120261
    {'degree': 16, 'field': [54756, 395460, 1215786, -2285790, -920595, 1737762, 532152, -722874, -86864, 148582, -1178, -13970, 1024, 574, -62, -8, 1], 'lmfdb_label': '159120.b1', 'torsion': [12]}
  • id: 7120258
    {'degree': 16, 'field': [138650625, 0, -345652500, 0, 255878500, 0, -70725000, 0, 7983375, 0, -441400, 0, 12660, 0, -180, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [2, 8]}
  • id: 7120260
    {'degree': 16, 'field': [213890625, 0, 392194500, 0, 101100100, 0, -99986100, 0, 4522950, 0, -25780, 0, -60, 0, -60, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [12]}
  • id: 7120257
    {'degree': 16, 'field': [7573350625, 0, -387261250, 0, -52776350, 0, -6148000, 0, 670831, 0, 20576, 0, -638, 0, 14, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [2, 8]}
  • id: 7120256
    {'degree': 16, 'field': [26984961441, 0, -5123774628, 0, 477733830, 0, -22366848, 0, 753079, 0, -8792, 0, 1890, 0, 28, 0, 1], 'lmfdb_label': '159120.b1', 'torsion': [4, 4]}
  • id: 7120259
    {'degree': 16, 'field': [280128849984, 0, -5438566884960, 0, 485660829268, 0, -16020389148, 0, 99163125, 0, 2265662, 0, -24105, 0, -66, 0, 1], 'lmfdb_label': '159120.b1', '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: 3935762
    {'conductor': 159120, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '159120.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3935763
    {'conductor': 159120, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '159120.b1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3935764
    {'conductor': 159120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '159120.b1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3935765
    {'conductor': 159120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '159120.b1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3935766
    {'conductor': 159120, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '159120.b1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

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

  
  
  • id: 2693383
    {'adelic_gens': [[1256, 3, 5, 2], [192, 967, 167, 120], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [976, 203, 1369, 1398], [1553, 8, 1552, 9], [7, 6, 1554, 1555], [1036, 1559, 497, 1554], [1204, 1, 1463, 6]], 'adelic_image': '1560.48.0.?', 'conductor': 159120, 'lmfdb_label': '159120.b1', 'prime': 0}
  • id: 606408
    {'conductor': 159120, 'elladic_image': '4.6.0.1', 'lmfdb_label': '159120.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 159120.b does not appear in ec_padic