Elliptic curve data - 174240.k1

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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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '174240eg', 'Clabel': '174240eg2', 'Cnumber': 2, 'abc_quality': 0.8651743910678557, 'absD': 14851675008624960000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 264, 'ainvs': [0, 0, 0, -682803, 113057802], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 174240, 'degree': 4460544, 'elladic_images': ['8.6.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3755618069398889921230291445', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [1481544, 625], 'lmfdb_iso': '174240.k', 'lmfdb_label': '174240.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -5643, 84942], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.f.1', '132.6.0.?', '264.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.2503748831264405657203477359', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 33], [3, 2, 19360], [5, 6, 34848], [11, 42, 1440]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.76667924957993016653278655776', 'prec': 107}, 'szpiro_ratio': 4.3018458104541, '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, -2, 0, 0, 0, 0, 0, -6, 0, 0, 0, -6, 0, -8, 0], 'aplist': [0, 0, -1, -2, 0, -6, -6, -8, -2, -6, 8, 2, -6, -4, -6, 2, -12, -10, -4, -6, -4, -10, 16, 16, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 174240, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '174240.k', 'trace_hash': 1407640940866824939}
• 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': '0.0086419794976797216020964314741', 'prec': 110}, 'conductor': 174240, 'gens': [[2326, 105400, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '6.2503748831264405657203477359', 'prec': 100}], 'lmfdb_label': '174240.k1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.20043669350448717863413730019', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5056089494747184760963386694464706130', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[726, 0, 1]], 'xcoord_integral_points': [726, 2326]}
• lmfdb_label 174240.k1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7730206
    {'degree': 2, 'field': [-66, 0, 1], 'lmfdb_label': '174240.k1', 'torsion': [2, 2]}
  • id: 7730207
    {'degree': 4, 'field': [66, 0, -33, 0, 1], 'lmfdb_label': '174240.k1', 'torsion': [4]}
  • id: 7730208
    {'degree': 8, 'field': [289, 0, -866, 0, 426, 0, -50, 0, 1], 'lmfdb_label': '174240.k1', 'torsion': [2, 4]}
  • id: 7730209
    {'degree': 8, 'field': [3844, 0, -560, 0, 156, 0, -8, 0, 1], 'lmfdb_label': '174240.k1', 'torsion': [2, 4]}
  • id: 7730210
    {'degree': 8, 'field': [9585, -20196, 6228, 0, 450, -132, -12, 0, 1], 'lmfdb_label': '174240.k1', 'torsion': [6]}
  • id: 7730211
    {'degree': 16, 'field': [2500, 0, -107500, 0, 18650, 0, 42350, 0, 6781, 0, -6116, 0, -274, 0, -26, 0, 1], 'lmfdb_label': '174240.k1', 'torsion': [8]}
  • id: 7730212
    {'degree': 16, 'field': [329422500, 0, 0, 0, 9583200, 0, -223608, 0, -277332, 0, 23232, 0, -44, 0, -44, 0, 1], 'lmfdb_label': '174240.k1', '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: 4311112
    {'conductor': 174240, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '174240.k1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4311113
    {'conductor': 174240, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '174240.k1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4311114
    {'conductor': 174240, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '174240.k1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4311115
    {'conductor': 174240, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '174240.k1', 'prime': 11, '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: 2786962
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [52, 1, 119, 0], [1, 4, 0, 1], [92, 1, 175, 0], [261, 4, 260, 5], [2, 1, 131, 0], [233, 34, 32, 231]], 'adelic_image': '264.12.0.?', 'conductor': 174240, 'lmfdb_label': '174240.k1', 'prime': 0}
  • id: 656183
    {'conductor': 174240, 'elladic_image': '8.6.0.2', 'lmfdb_label': '174240.k1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 174240.k does not appear in ec_padic