Elliptic curve data - 975.f3

Formats: - HTML - YAML - JSON - 2025-04-22T04:00:48.900731

• 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': '975g', 'Clabel': '975g2', 'Cnumber': 2, 'abc_quality': 0.9140273049268122, 'absD': 23765625, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 780, 'ainvs': [1, 0, 0, -113, -408], 'analytic_rank': 0, 'bad_primes': [3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 975, 'degree': 256, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.13977890380869007964298658871', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [10218313, 1521], 'lmfdb_iso': '975.f', 'lmfdb_label': '975.f3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -4, -5], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0.a.1', '20.12.0-2.a.1.1', '52.12.0.b.1', '60.24.0-12.a.1.1', '156.24.0.?', '260.24.0.?', '780.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 325], [5, 14, 39], [13, 14, 75]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.66494005240836010765739307790', 'prec': 107}, 'szpiro_ratio': 3.7481371452962744, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 1, -1, 0, -1, 4, 3, 1, 0, 4, -1, -1, -4, 0, -1, -2, -1, 0, 0], 'aplist': [-1, 1, 0, 4, 4, -1, -2, 0, 0, -10, 4, 2, 6, 12, 0, -6, 12, -2, 8, 0, -2, 8, -4, -2, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 975, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '975.f', 'trace_hash': 1467437157713976558}
• 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': '0.75611801717074569694243177570', 'prec': 103}, 'conductor': 975, 'gens': [], 'heights': [], 'lmfdb_label': '975.f3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.4788241842231084049928311492', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4788241842231084049928311492407490813', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-8, 4, 1], [12, -6, 1]], 'xcoord_integral_points': [-8, 12]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 0], '5': 'a', '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '975.f3'}
• ec_torsion_growth •

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

  
  
  • id: 47459
    {'degree': 4, 'field': [4, 0, -9, 0, 1], 'lmfdb_label': '975.f3', 'torsion': [2, 4]}
  • id: 47458
    {'degree': 4, 'field': [4, 0, 1, 0, 1], 'lmfdb_label': '975.f3', 'torsion': [2, 4]}
  • id: 47457
    {'degree': 4, 'field': [400, 0, 25, 0, 1], 'lmfdb_label': '975.f3', 'torsion': [2, 4]}
  • id: 47460
    {'degree': 8, 'field': [-111, -279, -121, 126, 75, -3, -9, 0, 1], 'lmfdb_label': '975.f3', 'torsion': [2, 6]}
  • id: 47464
    {'degree': 16, 'field': [1, 0, -12, 0, -33, 0, 12, 0, 208, 0, 12, 0, -33, 0, -12, 0, 1], 'lmfdb_label': '975.f3', 'torsion': [2, 8]}
  • id: 47463
    {'degree': 16, 'field': [256, 0, 256, 0, 688, 0, 16, 0, -287, 0, 4, 0, 43, 0, 4, 0, 1], 'lmfdb_label': '975.f3', 'torsion': [2, 8]}
  • id: 47462
    {'degree': 16, 'field': [256, 0, 2560, 0, 24208, 0, 42880, 0, 68248, 0, 10720, 0, 1513, 0, 40, 0, 1], 'lmfdb_label': '975.f3', 'torsion': [2, 8]}
  • id: 47461
    {'degree': 16, 'field': [59536, 0, -109540, 0, 63833, 0, -12936, 0, 1544, 0, -294, 0, 56, 0, -4, 0, 1], 'lmfdb_label': '975.f3', '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: 13488
    {'conductor': 975, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '975.f3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 13489
    {'conductor': 975, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '975.f3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 13490
    {'conductor': 975, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '975.f3', 'prime': 13, '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: 1670730
    {'adelic_gens': [[1, 0, 4, 1], [391, 160, 470, 321], [623, 0, 0, 779], [521, 160, 730, 321], [1, 4, 0, 1], [301, 470, 0, 1], [777, 4, 776, 5]], 'adelic_image': '780.48.0.?', 'conductor': 975, 'lmfdb_label': '975.f3', 'prime': 0}
  • id: 4582
    {'conductor': 975, 'elladic_image': '2.6.0.1', 'lmfdb_label': '975.f3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 975.f does not appear in ec_padic