Elliptic curve data - 1575.b1

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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': '1575b', 'Clabel': '1575b2', 'Cnumber': 2, 'abc_quality': 0.926249656518835, 'absD': 92302505859375, 'adelic_genus': 3, 'adelic_index': 96, 'adelic_level': 1680, 'ainvs': [1, -1, 1, -14555, -489428], 'analytic_rank': 0, 'bad_primes': [3, 5, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1575, 'degree': 3840, 'elladic_images': ['8.12.0.29'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3876576982126215110977657311', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [8869743, 2401], 'lmfdb_iso': '1575.b', 'lmfdb_label': '1575.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -65, 162], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.e.1', '8.12.0.s.1', '48.24.0.l.2', '56.24.0.dm.1', '60.12.0.bk.1', '80.24.0.?', '120.24.0.?', '240.48.0.?', '336.48.1.?', '560.48.1.?', '840.48.1.?', '1680.96.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 15], [3, 2, 175], [5, 14, 63], [7, 8, 225]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.64337995261403603839923769651', 'prec': 107}, 'szpiro_ratio': 5.483639001686581, '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, -1, 0, -1, 0, 0, -1, 3, 0, 0, 0, 0, 4, 1, 0, -1, -2, 0, 0, 0], 'aplist': [-1, 0, 0, -1, 0, 4, -2, 0, 0, -8, -4, 8, -4, 8, 12, -6, -8, 10, 8, 16, 12, -8, -16, 12, 4], 'class_deg': 2, 'class_size': 2, 'conductor': 1575, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1575.b', 'trace_hash': 1134750248174590471}
• 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': '0.062329814988387864297046961627', 'prec': 107}, 'conductor': 1575, 'gens': [], 'heights': [], 'lmfdb_label': '1575.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.44347372139664309490845041556', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.88694744279328618981690083111182023024', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-149, 145, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': 'a', '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '1575.b1'}
• ec_torsion_growth •

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

  
  
  • id: 77798
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '1575.b1', 'torsion': [2, 2]}
  • id: 77799
    {'degree': 4, 'field': [15, 0, 0, 0, 1], 'lmfdb_label': '1575.b1', 'torsion': [4]}
  • id: 77802
    {'degree': 8, 'field': [-69, 84, -108, 47, -20, -7, 7, -4, 1], 'lmfdb_label': '1575.b1', 'torsion': [6]}
  • id: 77801
    {'degree': 8, 'field': [16, -8, 2, 10, 1, -10, 8, -4, 1], 'lmfdb_label': '1575.b1', 'torsion': [2, 4]}
  • id: 77800
    {'degree': 8, 'field': [16, 0, -32, 0, 9, 0, -8, 0, 1], 'lmfdb_label': '1575.b1', 'torsion': [2, 4]}
  • id: 77805
    {'degree': 16, 'field': [81, 0, -1053, 0, -999, 0, -2544, 0, 1014, 0, 3, 0, 79, 0, 19, 0, 1], 'lmfdb_label': '1575.b1', 'torsion': [2, 6]}
  • id: 77804
    {'degree': 16, 'field': [256, 0, -976, 0, 800, 0, 101, 0, 529, 0, 106, 0, 50, 0, -11, 0, 1], 'lmfdb_label': '1575.b1', 'torsion': [8]}
  • id: 77803
    {'degree': 16, 'field': [2116, -4784, 5408, -5992, 4808, -1672, -24, 924, -1307, 732, -216, -4, 98, -76, 32, -8, 1], 'lmfdb_label': '1575.b1', 'torsion': [4, 4]}
• 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: 24276
    {'conductor': 1575, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '1575.b1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 24277
    {'conductor': 1575, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '1575.b1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 24278
    {'conductor': 1575, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1575.b1', 'prime': 7, '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: 1674271
    {'adelic_gens': [[1136, 1, 559, 0], [1, 0, 8, 1], [7, 8, 48, 55], [1, 8, 0, 1], [1, 4, 4, 17], [241, 16, 964, 65], [1673, 8, 1672, 9], [16, 1055, 1311, 16], [211, 226, 210, 211], [352, 5, 387, 16]], 'adelic_image': '1680.96.3.?', 'conductor': 1575, 'lmfdb_label': '1575.b1', 'prime': 0}
  • id: 7500
    {'conductor': 1575, 'elladic_image': '8.12.0.29', 'lmfdb_label': '1575.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1575.b does not appear in ec_padic