Elliptic curve data - 576.d6

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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': '576d', 'Clabel': '576d6', 'Cnumber': 6, 'abc_quality': 1.1597991410868231, 'absD': 626913312768, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 48, 'ainvs': [0, 0, 0, 564, 37744], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 576, 'degree': 512, 'elladic_images': ['16.96.0.250'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.94367462909411553716446012382', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [207646, 6561], 'lmfdb_iso': '576.d', 'lmfdb_label': '576.d6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 16, -180], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0.m.1', '12.12.0-4.c.1.2', '16.96.0-8.m.1.3', '24.96.0-8.m.1.2', '48.192.1-48.w.2.8'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 8, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.58759002103319516354090800004', 'prec': 107}, 'szpiro_ratio': 5.44363169850947, '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, 4, 0], 'aplist': [0, 0, -2, 0, 4, 2, -2, 4, 8, 6, 8, -6, 6, -4, 0, -2, 4, 2, 4, -8, 10, -8, -4, 6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 576, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '576.d', 'trace_hash': 1671394830863646620}
• 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': '0.15147279241380995335677055559', 'prec': 103}, 'conductor': 576, 'gens': [], 'heights': [], 'lmfdb_label': '576.d6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.68820470050109284938672190020', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3764094010021856987734438004014166847', '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'}, 'iwp0': 3, 'lmfdb_label': '576.d6'}
• ec_torsion_growth •

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

  
  
  • id: 26283
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [8]}
  • id: 26284
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '576.d6', 'torsion': [4]}
  • id: 26282
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [2, 2]}
  • id: 26285
    {'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [2, 8]}
  • id: 26290
    {'degree': 8, 'field': [-3, 0, -6, 0, 18, 0, -4, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [6]}
  • id: 26288
    {'degree': 8, 'field': [1, 0, 0, 0, -10, 0, 0, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [16]}
  • id: 26287
    {'degree': 8, 'field': [4, 0, 0, 0, 2, 0, 0, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [8]}
  • id: 26286
    {'degree': 8, 'field': [9, 0, 12, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [2, 4]}
  • id: 26289
    {'degree': 8, 'field': [36, 0, 24, 0, 10, 0, 4, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [2, 16]}
  • id: 26291
    {'degree': 16, 'field': [1, 0, -4, 0, 8, 0, -24, 0, 47, 0, -24, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [4, 8]}
  • id: 26292
    {'degree': 16, 'field': [1, 0, -4, 0, 8, 0, 36, 0, 62, 0, 36, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [2, 16]}
  • id: 26293
    {'degree': 16, 'field': [4, 0, 64, 0, -20, 0, 64, 0, -56, 0, 4, 0, 16, 0, 4, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [2, 6]}
  • id: 26295
    {'degree': 16, 'field': [9, 0, -30, 0, 82, 0, -60, 0, 39, 0, -20, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [12]}
  • id: 26294
    {'degree': 16, 'field': [324, 0, -1296, 0, 756, 0, -312, 0, 156, 0, -60, 0, 16, 0, -8, 0, 1], 'lmfdb_label': '576.d6', 'torsion': [24]}
• 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: 6754
    {'conductor': 576, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '576.d6', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6755
    {'conductor': 576, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '576.d6', 'prime': 3, '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: 1668451
    {'adelic_gens': [[1, 0, 16, 1], [31, 32, 8, 15], [1, 16, 0, 1], [22, 37, 9, 34], [4, 7, 21, 22], [15, 2, 46, 35], [5, 4, 44, 45], [33, 16, 32, 17]], 'adelic_image': '48.192.1.?', 'conductor': 576, 'lmfdb_label': '576.d6', 'prime': 0}
  • id: 2602
    {'conductor': 576, 'elladic_image': '16.96.0.250', 'lmfdb_label': '576.d6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 576.d does not appear in ec_padic