Elliptic curve data - 270504.a1

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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': '270504a', 'Clabel': '270504a2', 'Cnumber': 2, 'abc_quality': 0.9152444177905785, 'absD': 186434440705080502272, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1768, 'ainvs': [0, 0, 0, -24658347, 47125053830], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 270504, 'degree': 34537472, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9176925517407418524525728258', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [9365216434, 1053], 'lmfdb_iso': '270504.a', 'lmfdb_label': '270504.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -9480, -358416], 'min_quad_twist_disc': -51, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '68.6.0.c.1', '104.6.0.?', '1768.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '15.351205883241263114574797666', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1989], [3, 8, 30056], [13, 14, 20808], [17, 98, 936]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.39190851614875825373133020074', 'prec': 107}, 'szpiro_ratio': 5.010814664154815, '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, -4, 0, -4, 0, 0, 0, 6, 0, -1, 0, 0, 0, 0, 0, 4, 0], 'aplist': [0, 0, -4, -4, 6, -1, 0, 4, 6, -6, 0, 0, 6, 0, -12, 10, 4, 6, 12, 8, 6, -14, -4, 6, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 270504, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '270504.a', 'trace_hash': 215701854949082336}
• 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': '0.0029222976564267171836776104524', 'prec': 110}, 'conductor': 270504, 'gens': [[5150729, 10594311091, 22]], 'heights': [{'__RealLiteral__': 0, 'data': '15.351205883241263114574797666', 'prec': 100}], 'lmfdb_label': '270504.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.17253330686587591526962299852', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2971886308290091308347933035685678526', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[2890, 0, 1]], 'xcoord_integral_points': [2890]}
• lmfdb_label 270504.a1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11557388
    {'degree': 2, 'field': [-442, 0, 1], 'lmfdb_label': '270504.a1', 'torsion': [2, 2]}
  • id: 11557389
    {'degree': 4, 'field': [15912, 0, -255, 0, 1], 'lmfdb_label': '270504.a1', 'torsion': [4]}
  • id: 11557390
    {'degree': 8, 'field': [169, 0, -19422, 0, 13610, 0, -270, 0, 1], 'lmfdb_label': '270504.a1', 'torsion': [2, 4]}
  • id: 11557392
    {'degree': 8, 'field': [2217212, -1649912, 620740, -160864, 23188, -1004, -52, -2, 1], 'lmfdb_label': '270504.a1', 'torsion': [6]}
  • id: 11557391
    {'degree': 8, 'field': [179663238, -611568, 575304, 72480, -36119, -148, 54, -4, 1], 'lmfdb_label': '270504.a1', 'torsion': [2, 4]}
  • id: 11557393
    {'degree': 16, 'field': [2961101056, 0, -2265371932, 0, 577226129, 0, -65926926, 0, 3635339, 0, -92880, 0, 2315, 0, -94, 0, 1], 'lmfdb_label': '270504.a1', 'torsion': [8]}
  • id: 11557394
    {'degree': 16, 'field': [968427223569, 0, -5287078267848, 0, 4397184496744, 0, -64035472956, 0, 2660132670, 0, 11746384, 0, 156156, 0, 156, 0, 1], 'lmfdb_label': '270504.a1', '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: 6702914
    {'conductor': 270504, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '270504.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6702915
    {'conductor': 270504, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '270504.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6702916
    {'conductor': 270504, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '270504.a1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6702917
    {'conductor': 270504, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '270504.a1', '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: 3374105
    {'adelic_gens': [[2, 1, 883, 0], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1765, 4, 1764, 5], [1, 4, 0, 1], [1226, 1, 271, 0], [420, 1, 1663, 0], [665, 1106, 1104, 663]], 'adelic_image': '1768.12.0.?', 'conductor': 270504, 'lmfdb_label': '270504.a1', 'prime': 0}
  • id: 966924
    {'conductor': 270504, 'elladic_image': '2.3.0.1', 'lmfdb_label': '270504.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 270504.a does not appear in ec_padic