Elliptic curve data - 8450.r4

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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': '8450m', 'Clabel': '8450m1', 'Cnumber': 1, 'abc_quality': 0.9356398193134444, 'absD': 1254970340000000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 1040, 'ainvs': [1, -1, 1, -28255, -653753], 'analytic_rank': 0, 'bad_primes': [2, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 8450, 'degree': 32256, 'elladic_images': ['16.48.0.41'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5898334844702245133753611973', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [33076161, 16640], 'lmfdb_iso': '8450.r', 'lmfdb_label': '8450.r4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -7, -1], 'min_quad_twist_disc': 65, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.o.1.8', '16.48.0-16.i.1.8', '130.6.0.?', '260.24.0.?', '520.96.0.?', '1040.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 4225], [5, 18, 338], [13, 98, 50]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.49736015047759404195176219010', 'prec': 107}, 'szpiro_ratio': 4.684916359474791, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 0, 1, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 1, -2, -3, 8, 0], 'aplist': [1, 0, 0, 0, 0, 0, -2, 8, 4, -2, 4, 6, -10, 0, 8, -6, -8, -2, 4, 12, 10, -8, 12, -10, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 8450, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '8450.r', 'trace_hash': 1647095691927246879}
• 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': '0.041599506742342309153949802743', 'prec': 107}, 'conductor': 8450, 'gens': [], 'heights': [], 'lmfdb_label': '8450.r4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.38815771047043339791209771948', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1052616837634671832967817558517473706', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[439, 8230, 1]], 'xcoord_integral_points': [179, 439]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '5': 'a', '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '8450.r4'}
• ec_torsion_growth •

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

  
  
  • id: 442329
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '8450.r4', 'torsion': [2, 4]}
  • id: 442330
    {'degree': 4, 'field': [16, 4, -24, -1, 1], 'lmfdb_label': '8450.r4', 'torsion': [2, 8]}
  • id: 442333
    {'degree': 8, 'field': [16, -256, 232, 47, -20, -7, 7, -4, 1], 'lmfdb_label': '8450.r4', 'torsion': [12]}
  • id: 442332
    {'degree': 8, 'field': [16, -56, 98, -86, 33, 6, 8, -4, 1], 'lmfdb_label': '8450.r4', 'torsion': [2, 8]}
  • id: 442331
    {'degree': 8, 'field': [256, 32, 2, -70, 41, -10, 8, -4, 1], 'lmfdb_label': '8450.r4', 'torsion': [4, 4]}
  • id: 442336
    {'degree': 16, 'field': [64, -400, 1106, 342, -2167, 2962, -700, -2128, 3471, -2324, 866, -2, -89, 18, 8, -4, 1], 'lmfdb_label': '8450.r4', 'torsion': [2, 16]}
  • id: 442334
    {'degree': 16, 'field': [4096, 1024, 1152, -12928, 1152, -1136, 4882, -34, 2405, -246, 84, -198, 2, -2, 2, 0, 1], 'lmfdb_label': '8450.r4', 'torsion': [4, 8]}
  • id: 442337
    {'degree': 16, 'field': [4096, 1024, 10496, 0, 12800, 16208, 2416, 1296, -4160, -1380, 1480, -581, 68, 105, -25, -4, 1], 'lmfdb_label': '8450.r4', 'torsion': [2, 12]}
  • id: 442335
    {'degree': 16, 'field': [7640, 5880, -168735, 309230, -204865, 203260, -116315, 43490, -22949, 7328, 5043, -4174, 525, 236, -57, -2, 1], 'lmfdb_label': '8450.r4', 'torsion': [2, 16]}
• 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: 176206
    {'conductor': 8450, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '8450.r4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 176207
    {'conductor': 8450, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '8450.r4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 176208
    {'conductor': 8450, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '8450.r4', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1719904
    {'adelic_gens': [[15, 166, 754, 995], [1, 536, 398, 1039], [1, 16, 0, 1], [1025, 16, 1024, 17], [1, 8, 8, 65], [1, 16, 268, 389], [466, 1037, 867, 1020], [1, 0, 16, 1], [824, 1031, 809, 1014]], 'adelic_image': '1040.192.3.?', 'conductor': 8450, 'lmfdb_label': '8450.r4', 'prime': 0}
  • id: 41456
    {'conductor': 8450, 'elladic_image': '16.48.0.41', 'lmfdb_label': '8450.r4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 8450.r does not appear in ec_padic