Elliptic curve data - 180999.f1

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• 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': '180999e', 'Clabel': '180999e5', 'Cnumber': 5, 'abc_quality': 0.958227029320478, 'absD': 21518994346655338262457, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 74256, 'ainvs': [1, -1, 1, -61720691, 186517444650], 'analytic_rank': 1, 'bad_primes': [3, 7, 13, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 180999, 'degree': 16515072, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2136675058414821153396170096', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [7389727131216686257, 6115533215337], 'lmfdb_iso': '180999.f', 'lmfdb_label': '180999.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -40579, -3160960], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '34.6.0.a.1', '48.24.0-8.n.1.2', '68.12.0.g.1', '112.24.0.?', '136.24.0.?', '156.12.0.?', '168.24.0.?', '208.24.0.?', '312.24.0.?', '336.48.0.?', '624.48.0.?', '728.24.0.?', '816.48.0.?', '1456.48.0.?', '1904.48.0.?', '2184.48.0.?', '2652.24.0.?', '2856.48.0.?', '3536.48.0.?', '4368.96.0.?', '5304.48.0.?', '5712.96.0.?', '10608.96.0.?', '12376.48.0.?', '24752.96.0.?', '37128.96.0.?', '74256.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.4472155614736627441780802233', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3818866827766589016152506704', 'prec': 100}, 'szpiro_ratio': 5.4044819604995125, '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, -1, 0, -1, -2, 0, 1, 3, 0, 2, -4, 0, 0, -1, 0, -1, -1, 0, 4, 2], 'aplist': [-1, 0, -2, 1, -4, 0, -1, 4, 0, -6, 0, 2, 2, 12, 0, 10, 12, -10, -4, 8, -10, -8, 4, 10, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 180999, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '180999.f', 'trace_hash': 114309453713365491}
• 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': '0.0016167537281564104874675068382', 'prec': 110}, 'conductor': 180999, 'gens': [[4745, 19299, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '6.4472155614736627441780802233', 'prec': 100}], 'lmfdb_label': '180999.f1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12005781252662096122095559222', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0961543887924732034955969323592749199', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[18539, -18543, 2]], 'xcoord_integral_points': [4745]}
• lmfdb_label 180999.f1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8006489
    {'degree': 2, 'field': [-663, 0, 1], 'lmfdb_label': '180999.f1', 'torsion': [4]}
  • id: 8006488
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '180999.f1', 'torsion': [4]}
  • id: 8006487
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '180999.f1', 'torsion': [2, 2]}
  • id: 8006490
    {'degree': 4, 'field': [1186, 86, -85, -2, 1], 'lmfdb_label': '180999.f1', 'torsion': [2, 4]}
  • id: 8006492
    {'degree': 4, 'field': [1225, 0, -112, 0, 1], 'lmfdb_label': '180999.f1', 'torsion': [8]}
  • id: 8006491
    {'degree': 4, 'field': [455625, 0, -1506, 0, 1], 'lmfdb_label': '180999.f1', 'torsion': [8]}
  • id: 8006496
    {'degree': 8, 'field': [-34967, 31568, -32138, 1139, -566, -7, 7, -4, 1], 'lmfdb_label': '180999.f1', 'torsion': [6]}
  • id: 8006494
    {'degree': 8, 'field': [13026, -2028, 2662, -1308, 755, -124, 46, -4, 1], 'lmfdb_label': '180999.f1', 'torsion': [8]}
  • id: 8006495
    {'degree': 8, 'field': [510682, 306828, -290954, -31508, 15155, 716, -234, -4, 1], 'lmfdb_label': '180999.f1', 'torsion': [2, 8]}
  • id: 8006493
    {'degree': 8, 'field': [55007992, -873652, 859258, 28748, -14273, -124, 46, -4, 1], 'lmfdb_label': '180999.f1', 'torsion': [2, 4]}
  • id: 8006498
    {'degree': 16, 'field': [169676676, 0, -65237640, 0, 21450256, 0, -3004204, 0, 500373, 0, -48944, 0, 2634, 0, -76, 0, 1], 'lmfdb_label': '180999.f1', 'torsion': [2, 8]}
  • id: 8006503
    {'degree': 16, 'field': [6438592261, 8308846216, -9887706750, 4135827642, -4593343176, 3256988400, -1469185625, 340920904, -100581000, 10415760, -2265015, 99120, -16429, -70, 30, -8, 1], 'lmfdb_label': '180999.f1', 'torsion': [12]}
  • id: 8006501
    {'degree': 16, 'field': [28913261521, 0, -6963175708, 0, 898313392, 0, 36994733, 0, -2812532, 0, -76561, 0, -635, 0, -34, 0, 1], 'lmfdb_label': '180999.f1', 'torsion': [2, 6]}
  • id: 8006497
    {'degree': 16, 'field': [57725749237, -112177297882, 80579082986, -28340302118, 5779448168, -126261272, -118867056, 13711206, 4677529, -994872, 144240, 5302, -172, 82, 86, -4, 1], 'lmfdb_label': '180999.f1', 'torsion': [4, 4]}
  • id: 8006502
    {'degree': 16, 'field': [83584944261, -32705879778, 34379183619, -3305615190, 1549714746, 125414442, -44616509, 2362492, -544299, -10540, -18187, 10992, -1741, -70, 30, -8, 1], 'lmfdb_label': '180999.f1', 'torsion': [12]}
  • id: 8006500
    {'degree': 16, 'field': [3378702446895850, 152605054897160, -148940283037348, -7266950407080, 3477772599686, 184664505256, -57945581036, -3050261496, 708719467, 35300712, -6468140, -317128, 48062, 2184, -292, -8, 1], 'lmfdb_label': '180999.f1', 'torsion': [16]}
  • id: 8006499
    {'degree': 16, 'field': [30911634015800209, 0, -17783111612149688, 0, 973960169581672, 0, -20930659667456, 0, 217509869374, 0, -1135404872, 0, 2844520, 0, -2912, 0, 1], 'lmfdb_label': '180999.f1', 'torsion': [16]}
• 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: 4480059
    {'conductor': 180999, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '180999.f1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4480060
    {'conductor': 180999, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '180999.f1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4480061
    {'conductor': 180999, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '180999.f1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4480062
    {'conductor': 180999, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '180999.f1', 'prime': 17, '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: 2828813
    {'adelic_gens': [[8752, 5, 21795, 74242], [13, 16, 18308, 18249], [1, 16, 0, 1], [46423, 16, 64718, 18249], [42445, 16, 20960, 73941], [74241, 16, 74240, 17], [15, 2, 74158, 74243], [1, 0, 16, 1], [24739, 74240, 49760, 315], [28559, 74240, 5704, 74127], [5, 4, 74252, 74253]], 'adelic_image': '74256.192.1.?', 'conductor': 180999, 'lmfdb_label': '180999.f1', 'prime': 0}
  • id: 678856
    {'conductor': 180999, 'elladic_image': '8.12.0.5', 'lmfdb_label': '180999.f1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 180999.f does not appear in ec_padic