Elliptic curve data - 45504.p1

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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': '45504p', 'Clabel': '45504p2', 'Cnumber': 2, 'abc_quality': 0.8597299405419038, 'absD': 2385347346432, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 632, 'ainvs': [0, 0, 0, -5196, -123536], 'analytic_rank': 0, 'bad_primes': [2, 3, 79], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 45504, 'degree': 55296, 'elladic_images': ['8.6.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0985611178945857524344848907', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [81182737, 12482], 'lmfdb_iso': '45504.p', 'lmfdb_label': '45504.p1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -9, 5], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.b.1', '316.6.0.?', '632.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 2, 5056], [79, 80, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.49046579727938705738898590995', 'prec': 107}, 'szpiro_ratio': 3.4758606321455976, '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, -2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, -2, 0, -4, -2, 2, 0, 0, 8, 8, -4, 10, 2, 0, -8, 14, 0, -8, -8, 6, -1, 12, -6, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 45504, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '45504.p', 'trace_hash': 2249674948226939859}
• 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': '0.11112248297601362880585815373', 'prec': 103}, 'conductor': 45504, 'gens': [], 'heights': [], 'lmfdb_label': '45504.p1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.56813027117898230367311224249', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1362605423579646073462244849875456682', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-28, 0, 1]], 'xcoord_integral_points': [-28]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '79': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '45504.p1'}
• ec_torsion_growth •

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

  
  
  • id: 2222047
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '45504.p1', 'torsion': [2, 2]}
  • id: 2222048
    {'degree': 4, 'field': [288, 0, 21, 0, 1], 'lmfdb_label': '45504.p1', 'torsion': [4]}
  • id: 2222051
    {'degree': 8, 'field': [-972, 0, -378, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '45504.p1', 'torsion': [6]}
  • id: 2222049
    {'degree': 8, 'field': [196, 0, -128, 0, 50, 0, -16, 0, 1], 'lmfdb_label': '45504.p1', 'torsion': [2, 4]}
  • id: 2222050
    {'degree': 8, 'field': [1600, 0, -1392, 0, 1217, 0, 60, 0, 1], 'lmfdb_label': '45504.p1', 'torsion': [2, 4]}
  • id: 2222053
    {'degree': 16, 'field': [64, 0, -424, 0, 100, 0, -24, 0, 204, 0, 36, 0, 16, 0, -4, 0, 1], 'lmfdb_label': '45504.p1', 'torsion': [2, 6]}
  • id: 2222052
    {'degree': 16, 'field': [3469624000, -2822434304, 2448274264, -1275972224, 573538636, -193906556, 64945853, -15851746, 4262157, -754880, 177578, -23756, 4598, -500, 81, -2, 1], 'lmfdb_label': '45504.p1', '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: 1083629
    {'conductor': 45504, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '45504.p1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1083630
    {'conductor': 45504, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '45504.p1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1083631
    {'conductor': 45504, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '45504.p1', 'prime': 79, '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: 1967277
    {'adelic_gens': [[1, 2, 2, 5], [81, 554, 552, 79], [1, 4, 0, 1], [161, 4, 322, 9], [2, 1, 315, 0], [1, 0, 4, 1], [629, 4, 628, 5], [3, 4, 8, 11]], 'adelic_image': '632.12.0.?', 'conductor': 45504, 'lmfdb_label': '45504.p1', 'prime': 0}
  • id: 197220
    {'conductor': 45504, 'elladic_image': '8.6.0.6', 'lmfdb_label': '45504.p1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 45504.p does not appear in ec_padic