Elliptic curve data - 356160.bz1

Formats: - HTML - YAML - JSON - 2026-04-06T16:30:39.005316

• 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': '356160bz', 'Clabel': '356160bz3', 'Cnumber': 3, 'abc_quality': 1.0107688116183124, 'absD': 964140539827562535243939840, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, -1, 0, -523909505, -4367019529215], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 53], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 356160, 'degree': 176357376, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9300868830643793676362038626', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 51, 'isogeny_degrees': [1, 2, 4], 'jinv': [242668058425926391337530756, 14711617123833656848815], 'lmfdb_iso': '356160.bz', 'lmfdb_label': '356160.bz1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -130977376, -545942929840], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.1', '40.12.0-4.c.1.2', '56.12.0-4.c.1.4', '60.12.0.h.1', '120.24.0.?', '168.24.0.?', '280.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.396914362941911699424426385', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 15], [3, 4, 118720], [5, 6, 71232], [7, 8, 50880], [53, 54, 6720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.0058906423177856217465610340', 'prec': 100}, 'szpiro_ratio': 5.620224590054984, '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, 1, 0, -1, 0, 1, 0, -4, 0, 6, 0, -1, 0, -2, 0, 0, 0], 'aplist': [0, -1, 1, -1, -4, 6, -2, 0, -4, -6, -4, 2, -2, -4, 8, 1, -12, 10, -12, 0, 14, -8, 4, -10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 356160, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '356160.bz', 'trace_hash': 1098213152800254807}
• 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': '0.00038580682538856251361443554345', 'prec': 113}, 'conductor': 356160, 'gens': [[79804417, 385407639568, 51]], 'heights': [{'__RealLiteral__': 0, 'data': '11.396914362941911699424426385', 'prec': 100}], 'lmfdb_label': '356160.bz1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.031675946121433325460546025611', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.7761287249782017153413295176756924229', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[26271, 0, 1]], 'xcoord_integral_points': [26271]}
• lmfdb_label 356160.bz1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 14843238
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [2, 2]}
  • id: 14843240
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [4]}
  • id: 14843239
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [4]}
  • id: 14843241
    {'degree': 4, 'field': [1, 0, -8, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [2, 4]}
  • id: 14843245
    {'degree': 8, 'field': [-40368, 0, -34112, 0, -696, 0, 0, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [6]}
  • id: 14843243
    {'degree': 8, 'field': [1, 0, -14, 0, 30, 0, -14, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [8]}
  • id: 14843242
    {'degree': 8, 'field': [1, 0, 4, 0, -9, 0, 4, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [2, 4]}
  • id: 14843244
    {'degree': 8, 'field': [2601, 0, -294, 0, 46, 0, -14, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [8]}
  • id: 14843248
    {'degree': 16, 'field': [16, 0, -4320, 0, 22192, 0, -35712, 0, 23724, 0, -6672, 0, 844, 0, -48, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [2, 8]}
  • id: 14843246
    {'degree': 16, 'field': [225, 0, 900, 0, 870, 0, 660, 0, 451, 0, 196, 0, 66, 0, 16, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [4, 4]}
  • id: 14843247
    {'degree': 16, 'field': [292681, 0, -283552, 0, 245498, 0, -116724, 0, 40475, 0, -8244, 0, 998, 0, -52, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [2, 8]}
  • id: 14843250
    {'degree': 16, 'field': [1102500, 0, -792000, 0, 262300, 0, 46704, 0, -15528, 0, -1516, 0, -24, 0, -12, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [12]}
  • id: 14843251
    {'degree': 16, 'field': [2968729, 0, -2155832, 0, 412660, 0, 55116, 0, -21090, 0, -2376, 0, 88, 0, -20, 0, 1], 'lmfdb_label': '356160.bz1', 'torsion': [12]}
  • id: 14843249
    {'degree': 16, 'field': [432994268529, 0, -100331428248, 0, 4630443340, 0, 25346424, 0, -4031850, 0, -298984, 0, 4908, 0, -120, 0, 1], 'lmfdb_label': '356160.bz1', '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: 8816506
    {'conductor': 356160, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '356160.bz1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 8816507
    {'conductor': 356160, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '356160.bz1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 8816508
    {'conductor': 356160, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '356160.bz1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 8816509
    {'conductor': 356160, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '356160.bz1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8816510
    {'conductor': 356160, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '356160.bz1', 'prime': 53, '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: 3885733
    {'adelic_gens': [[101, 102, 302, 725], [568, 3, 565, 2], [1, 0, 8, 1], [833, 8, 832, 9], [1, 8, 0, 1], [1, 4, 4, 17], [241, 8, 124, 33], [736, 323, 739, 768], [508, 1, 191, 6], [7, 6, 834, 835]], 'adelic_image': '840.48.0.?', 'conductor': 356160, 'lmfdb_label': '356160.bz1', 'prime': 0}
  • id: 1229613
    {'conductor': 356160, 'elladic_image': '4.6.0.1', 'lmfdb_label': '356160.bz1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 356160.bz does not appear in ec_padic