Elliptic curve data - 7728.e1

Formats: - HTML - YAML - JSON - 2024-05-01T18:13:26.803368

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '7728g', 'Clabel': '7728g1', 'Cnumber': 1, 'abc_quality': 0.7434793360740976, 'absD': 1978368, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 966, 'ainvs': [0, -1, 0, 27, -51], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 23], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 7728, 'degree': 800, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.10468203241037256346640028056', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1], 'jinv': [512000, 483], 'lmfdb_iso': '7728.e', 'lmfdb_label': '7728.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, 2, 1], 'min_quad_twist_disc': -4, 'modell_images': [], 'modm_images': ['966.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.79782921297031787288363240202', 'prec': 107}, 'szpiro_ratio': 2.39749717200079, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 0, 0, 0, -1, 0, 1, 0, -1, 0, 2, 0, 0, 0, 4, 0, 3, 0], 'aplist': [0, -1, 0, -1, -1, 2, 4, 3, -1, -6, 2, -2, 1, 8, 5, 3, -5, 13, 0, 0, -16, 2, -6, 6, 10], 'class_deg': 1, 'class_size': 1, 'conductor': 7728, 'isogeny_matrix': [[1]], 'lmfdb_iso': '7728.e', 'trace_hash': 1209268214298030546}
• 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': '1.2328937700837337998730356953', 'prec': 100}, 'conductor': 7728, 'gens': [], 'heights': [], 'lmfdb_label': '7728.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.4340667301071313863730089260', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4340667301071313863730089260283796824', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [2, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '7728.e1'}
• ec_torsion_growth •

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

  
  
  • id: 404163
    {'degree': 3, 'field': [3, 7, -1, 1], 'lmfdb_label': '7728.e1', 'torsion': [2]}
  • id: 404164
    {'degree': 6, 'field': [1932, 0, 400, 0, 40, 0, 1], 'lmfdb_label': '7728.e1', 'torsion': [2, 2]}
  • id: 404165
    {'degree': 8, 'field': [-75, 0, -71, 0, 30, 0, 0, 0, 1], 'lmfdb_label': '7728.e1', 'torsion': [3]}
  • id: 404166
    {'degree': 12, 'field': [48432, 30208, -27200, -43456, -14152, 1904, 984, 8, 104, -28, -24, 0, 1], 'lmfdb_label': '7728.e1', 'torsion': [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: 159462
    {'conductor': 7728, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '7728.e1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 159463
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7728.e1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 159464
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7728.e1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 159465
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7728.e1', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  {'adelic_gens': [[1, 1, 965, 0], [323, 2, 323, 3], [925, 2, 925, 3], [1, 0, 2, 1], [1, 2, 0, 1], [965, 2, 964, 3], [829, 2, 829, 3]], 'adelic_image': '966.2.0.?', 'conductor': 7728, 'lmfdb_label': '7728.e1', 'prime': 0}
• lmfdb_iso 7728.e does not appear in ec_padic