Elliptic curve data - 212160.gu1

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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': '212160p', 'Clabel': '212160p1', 'Cnumber': 1, 'abc_quality': 0.9539622736558061, 'absD': 272241295073280000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1768, 'ainvs': [0, 1, 0, -1124065, -458394337], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 212160, 'degree': 2949120, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2393375922581837715701781561', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 176, 'isogeny_degrees': [1, 2], 'jinv': [2396726313900986596, 4154072495625], 'lmfdb_iso': '212160.gu', 'lmfdb_label': '212160.gu1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -281016, 57158784], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '34.6.0.a.1', '104.6.0.?', '1768.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.72574837306518833677487319064', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3151413515115900256805353275', 'prec': 100}, 'szpiro_ratio': 4.354714418398533, '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, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, -1, 0, -8, 0], 'aplist': [0, 1, 1, 0, 2, 1, -1, -8, -6, 0, 4, -2, 4, -4, 0, 6, 4, -8, 8, 4, 0, -10, 8, 6, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 212160, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '212160.gu', 'trace_hash': 382541557361781516}
• 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': '0.011348437786131776959915698520', 'prec': 107}, 'conductor': 212160, 'gens': [[-619, 780, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.72574837306518833677487319064', 'prec': 103}], 'lmfdb_label': '212160.gu1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14663811851351996546773143804', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.216548090290629295511876669219551035', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[-593, 0, 1]], 'xcoord_integral_points': [-619, -593, 2111, 28991]}
• lmfdb_label 212160.gu1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9262932
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '212160.gu1', 'torsion': [2, 2]}
  • id: 9262933
    {'degree': 4, 'field': [27, -2, 3, -2, 1], 'lmfdb_label': '212160.gu1', 'torsion': [4]}
  • id: 9262936
    {'degree': 8, 'field': [-30000, 0, 5600, 0, -600, 0, 0, 0, 1], 'lmfdb_label': '212160.gu1', 'torsion': [6]}
  • id: 9262934
    {'degree': 8, 'field': [1024, 0, 462, 0, -379, 0, -24, 0, 1], 'lmfdb_label': '212160.gu1', 'torsion': [2, 4]}
  • id: 9262935
    {'degree': 8, 'field': [2601, 0, 1054, 0, 151, 0, -14, 0, 1], 'lmfdb_label': '212160.gu1', 'torsion': [2, 4]}
  • id: 9262938
    {'degree': 16, 'field': [342560336, -263520128, 298765216, -46328832, -35933624, 67267136, -16352096, -5172896, 1249977, 37624, -16756, 5576, -1354, 168, -4, -8, 1], 'lmfdb_label': '212160.gu1', 'torsion': [2, 6]}
  • id: 9262937
    {'degree': 16, 'field': [547981281, 0, 214894620, 0, -1544994, 0, -14295096, 0, 2067251, 0, -93432, 0, -66, 0, 60, 0, 1], 'lmfdb_label': '212160.gu1', 'torsion': [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: 5257239
    {'conductor': 212160, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '212160.gu1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5257240
    {'conductor': 212160, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '212160.gu1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5257241
    {'conductor': 212160, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '212160.gu1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5257242
    {'conductor': 212160, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '212160.gu1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 5257243
    {'conductor': 212160, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '212160.gu1', '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: 3021079
    {'adelic_gens': [[210, 1, 1663, 0], [1, 2, 2, 5], [1, 4, 0, 1], [1765, 4, 1764, 5], [225, 1548, 1104, 663], [1, 0, 4, 1], [1497, 4, 1226, 9], [3, 4, 8, 11], [885, 4, 2, 9]], 'adelic_image': '1768.12.0.?', 'conductor': 212160, 'lmfdb_label': '212160.gu1', 'prime': 0}
  • id: 782015
    {'conductor': 212160, 'elladic_image': '2.3.0.1', 'lmfdb_label': '212160.gu1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 212160.gu does not appear in ec_padic