Elliptic curve data - 129472.bw1

Formats: - HTML - YAML - JSON - 2024-06-15T19:19:56.786612

• 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': '129472a', 'Clabel': '129472a1', 'Cnumber': 1, 'abc_quality': 1.0498004125880718, 'absD': 19107872719802212548608, 'adelic_genus': 9, 'adelic_index': 192, 'adelic_level': 1904, 'ainvs': [0, 0, 0, -14051180, 19151031216], 'analytic_rank': 1, 'bad_primes': [2, 7, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 129472, 'degree': 6684672, 'elladic_images': ['16.48.1.35'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0267914217169710043989970870', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 48, 'isogeny_degrees': [1, 2], 'jinv': [9869198625, 614656], 'lmfdb_iso': '129472.bw', 'lmfdb_label': '129472.bw1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -760, 7803], 'min_quad_twist_disc': 136, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.f.1', '8.24.0.bt.1', '16.48.1.cf.1', '34.6.0.a.1', '56.48.1.kd.1', '68.24.0.h.1', '112.96.3.?', '136.48.1.?', '272.96.3.?', '952.96.3.?', '1904.192.9.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '12.094322601137516773631910983', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.13783935716510901991400205859', 'prec': 107}, 'szpiro_ratio': 5.181132818215047, '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, 0, 0, -1, 0, -3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0], 'aplist': [0, 0, 0, -1, 0, -2, 0, 4, 8, -8, 8, 8, 8, -4, -8, -10, -12, 0, 4, -8, 8, 8, -4, 6, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 129472, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '129472.bw', 'trace_hash': 1397131760711281089}
• 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': '0.0023494292716871495842404169791', 'prec': 110}, 'conductor': 129472, 'gens': [[5522550, 11177542656, 29]], 'heights': [{'__RealLiteral__': 0, 'data': '12.094322601137516773631910983', 'prec': 100}], 'lmfdb_label': '129472.bw1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12004942209595029021296558800', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.8076657556341967787927573712175959350', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[1734, 0, 1]], 'xcoord_integral_points': [1734]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [1, 1, 0], '7': [3, 0], '11': [1, 1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '129472.bw1'}
• ec_torsion_growth •

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

  
  
  • id: 5886352
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '129472.bw1', 'torsion': [2, 2]}
  • id: 5886354
    {'degree': 4, 'field': [-68, 0, 0, 0, 1], 'lmfdb_label': '129472.bw1', 'torsion': [2, 4]}
  • id: 5886353
    {'degree': 4, 'field': [17, 0, 0, 0, 1], 'lmfdb_label': '129472.bw1', 'torsion': [4]}
  • id: 5886356
    {'degree': 8, 'field': [-13872, 0, -5202, 0, 408, 0, 0, 0, 1], 'lmfdb_label': '129472.bw1', 'torsion': [6]}
  • id: 5886355
    {'degree': 8, 'field': [324, 0, -200, 0, 40, 0, 4, 0, 1], 'lmfdb_label': '129472.bw1', 'torsion': [4, 4]}
  • id: 5886360
    {'degree': 16, 'field': [-35461304, 163315144, -253164138, 200410196, -152489314, 64162536, -23790164, 2126932, -617271, 59020, -14180, 1764, -658, 140, 0, -8, 1], 'lmfdb_label': '129472.bw1', 'torsion': [2, 6]}
  • id: 5886357
    {'degree': 16, 'field': [16, 0, 168, -200, -318, 652, -222, -620, 1233, -1188, 726, -308, 112, -56, 28, -8, 1], 'lmfdb_label': '129472.bw1', 'torsion': [8]}
  • id: 5886359
    {'degree': 16, 'field': [103684, 414736, -267288, -47488, -538032, 513112, 103372, -246136, 72533, -3072, -3856, 2688, -630, 56, 12, -8, 1], 'lmfdb_label': '129472.bw1', 'torsion': [2, 8]}
  • id: 5886358
    {'degree': 16, 'field': [5308144, -1841936, 5589564, -3921232, 3489394, -2159212, 1455956, -686548, 316983, -117872, 42960, -11124, 2870, -476, 88, -8, 1], 'lmfdb_label': '129472.bw1', 'torsion': [2, 8]}
• 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: 3192692
    {'conductor': 129472, 'conductor_valuation': 6, 'discriminant_valuation': 26, 'j_denominator_valuation': 8, 'kodaira_symbol': -20, 'lmfdb_label': '129472.bw1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 3192693
    {'conductor': 129472, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '129472.bw1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3192694
    {'conductor': 129472, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '129472.bw1', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 2507526
    {'adelic_gens': [[1, 16, 8, 1557], [5, 16, 64, 205], [1361, 4, 1100, 49], [1, 16, 0, 1], [11, 16, 1840, 1811], [1, 8, 8, 65], [1889, 16, 1888, 17], [1, 956, 12, 287], [1, 0, 16, 1], [1236, 5, 819, 44]], 'adelic_image': '1904.192.9.?', 'conductor': 129472, 'lmfdb_label': '129472.bw1', 'prime': 0}
  • id: 504305
    {'conductor': 129472, 'elladic_image': '16.48.1.35', 'lmfdb_label': '129472.bw1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 6790144
    {'lmfdb_iso': '129472.bw', 'p': 13, 'prec': 20, 'unit': 644526580963979170016, 'val': 1}
  • id: 6790137
    {'lmfdb_iso': '129472.bw', 'p': 19, 'prec': 20, 'unit': 1944472977070917914044165, 'val': 1}
  • id: 6790150
    {'lmfdb_iso': '129472.bw', 'p': 23, 'prec': 20, 'unit': 59770164627013780194778584, 'val': 1}
  • id: 6790153
    {'lmfdb_iso': '129472.bw', 'p': 29, 'prec': 20, 'unit': 5164807883263683805117159335, 'val': 1}
  • id: 6790154
    {'lmfdb_iso': '129472.bw', 'p': 31, 'prec': 20, 'unit': 1964732721272781826680922770, 'val': 1}
  • id: 6790140
    {'lmfdb_iso': '129472.bw', 'p': 37, 'prec': 20, 'unit': 411199740615943048440869717052, 'val': 1}
  • id: 6790142
    {'lmfdb_iso': '129472.bw', 'p': 41, 'prec': 20, 'unit': 3625392377124410880954479202628, 'val': 1}
  • id: 6790143
    {'lmfdb_iso': '129472.bw', 'p': 43, 'prec': 20, 'unit': 4968516075924095393204059750346, 'val': 1}
  • id: 6790152
    {'lmfdb_iso': '129472.bw', 'p': 47, 'prec': 20, 'unit': 3972943943959851577876916211549, 'val': 1}
  • id: 6790148
    {'lmfdb_iso': '129472.bw', 'p': 53, 'prec': 20, 'unit': 383973833783361827194681805389248, 'val': 1}
  • id: 6790146
    {'lmfdb_iso': '129472.bw', 'p': 59, 'prec': 20, 'unit': 1604687571746849056628183165435255, 'val': 1}
  • id: 6790139
    {'lmfdb_iso': '129472.bw', 'p': 67, 'prec': 20, 'unit': 3358675990058255836171094985792407, 'val': 1}
  • id: 6790141
    {'lmfdb_iso': '129472.bw', 'p': 71, 'prec': 20, 'unit': 109235701505511316118795392165693403, 'val': 1}
  • id: 6790149
    {'lmfdb_iso': '129472.bw', 'p': 73, 'prec': 20, 'unit': 139383046188790063111106660815109828, 'val': 1}
  • id: 6790145
    {'lmfdb_iso': '129472.bw', 'p': 79, 'prec': 20, 'unit': 410872539988512875589606147519493113, 'val': 1}
  • id: 6790147
    {'lmfdb_iso': '129472.bw', 'p': 83, 'prec': 20, 'unit': 485521978379925223943211034073958647, 'val': 1}
  • id: 6790151
    {'lmfdb_iso': '129472.bw', 'p': 89, 'prec': 20, 'unit': 8549916126704008790900686449205155891, 'val': 1}
  • id: 6790138
    {'lmfdb_iso': '129472.bw', 'p': 97, 'prec': 20, 'unit': 31242955067412450758572205638906953229, 'val': 1}