Elliptic curve data - 361920.a2

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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': '361920a', 'Clabel': '361920a2', 'Cnumber': 2, 'abc_quality': 0.8105362360141121, 'absD': 523944345600, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 45240, 'ainvs': [0, -1, 0, -2321, 56145], 'analytic_rank': 3, 'bad_primes': [2, 3, 5, 13, 29], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 361920, 'degree': 737280, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.95846235782774944131010636197', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [-84433792336, 31979025], 'lmfdb_iso': '361920.a', 'lmfdb_label': '361920.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -580, -6728], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '12.12.0-4.a.1.1', '7540.12.0.?', '15080.24.0.?', '22620.24.0.?', '45240.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 53, 'optimality': 0, 'potential_good_reduction': False, 'rank': 3, 'regulator': {'__RealLiteral__': 0, 'data': '1.1743957135084222426090461990', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.14979064717447991365666888694', 'prec': 103}, 'szpiro_ratio': 2.7632068354697745, '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, -4, 0, 1, 0, -4, 0, 1, 0, 1, 0, -6, 0, -4, 0], 'aplist': [0, -1, -1, -4, -4, 1, -6, -4, -6, -1, -4, -10, -10, 0, -6, -14, -2, -10, -16, -2, -14, -2, 8, 10, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 361920, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '361920.a', 'trace_hash': 1930776219383168419}
• 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': '0.14705851419540800458037221560', 'prec': 103}, 'conductor': 361920, 'gens': [[1, 232, 1], [-31, 312, 1], [8, 195, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.95411284789722006864184442433', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.0780976522379827563470203163', 'prec': 100}, {'__RealLiteral__': 0, 'data': '1.3165304988712271417696815766', 'prec': 100}], 'lmfdb_label': '361920.a2', 'ngens': 3, 'rank_bounds': [3, 3], 'real_period': {'__RealLiteral__': 0, 'data': '0.87134701752123275630429612822', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999998', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '16.372899237684541443484610017155514002', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-57, 0, 1]], 'xcoord_integral_points': [-57, -55, -37, -31, -5, 1, 8, 23, 24, 33, 41, 59, 64, 73, 88, 151, 193, 233, 320, 411, 521, 1223, 3713, 6729, 10473, 22679, 56123]}
• lmfdb_label 361920.a2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 15055434
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '361920.a2', 'torsion': [2, 2]}
  • id: 15055435
    {'degree': 4, 'field': [-36, 0, -86, 0, 1], 'lmfdb_label': '361920.a2', 'torsion': [4]}
  • id: 15055438
    {'degree': 8, 'field': [-3888, 0, -12384, 0, 216, 0, 0, 0, 1], 'lmfdb_label': '361920.a2', 'torsion': [6]}
  • id: 15055437
    {'degree': 8, 'field': [81, 0, 0, 0, 1867, 0, 0, 0, 1], 'lmfdb_label': '361920.a2', 'torsion': [2, 4]}
  • id: 15055436
    {'degree': 8, 'field': [3553225, 0, -22620, 0, -1741, 0, -12, 0, 1], 'lmfdb_label': '361920.a2', 'torsion': [2, 4]}
  • id: 15055439
    {'degree': 16, 'field': [6561, 0, 0, 0, -151227, 0, 0, 0, 3485608, 0, 0, 0, -1867, 0, 0, 0, 1], 'lmfdb_label': '361920.a2', 'torsion': [4, 4]}
  • id: 15055441
    {'degree': 16, 'field': [59049, 0, 0, 0, 2422548, 0, 0, 0, 2430, 0, 0, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '361920.a2', 'torsion': [2, 6]}
  • id: 15055440
    {'degree': 16, 'field': [178623225, 0, -824571900, 0, 679676670, 0, 406505700, 0, 72753531, 0, 4858532, 0, 45874, 0, 368, 0, 1], 'lmfdb_label': '361920.a2', '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: 8955112
    {'conductor': 361920, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '361920.a2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8955113
    {'conductor': 361920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '361920.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8955114
    {'conductor': 361920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '361920.a2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8955115
    {'conductor': 361920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '361920.a2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8955116
    {'conductor': 361920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '361920.a2', 'prime': 29, 'reduction_type': -1, '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: 3919172
    {'adelic_gens': [[3, 8, 10, 27], [1, 0, 8, 1], [10441, 2, 0, 1], [22619, 45232, 45238, 45223], [1, 8, 0, 1], [11309, 45236, 28273, 45231], [18097, 2, 0, 1], [30161, 8, 15082, 17], [5, 8, 48, 77], [37441, 6, 0, 1], [45233, 8, 45232, 9]], 'adelic_image': '45240.48.0.?', 'conductor': 361920, 'lmfdb_label': '361920.a2', 'prime': 0}
  • id: 1246533
    {'conductor': 361920, 'elladic_image': '4.6.0.5', 'lmfdb_label': '361920.a2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 361920.a does not appear in ec_padic