Elliptic curve data - 4650.bs2

Formats: - HTML - YAML - JSON - 2025-03-07T10:00:47.174559

• 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': '4650bs', 'Clabel': '4650bs1', 'Cnumber': 1, 'abc_quality': 0.9966102850167543, 'absD': 252467553375000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 120, 'ainvs': [1, 0, 0, -314638, -72130108], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 31], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4650, 'degree': 94080, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0883776714749716778182552145', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 44, 'isogeny_degrees': [1, 2], 'jinv': [-1763710408147661, 129263387328], 'lmfdb_iso': '4650.bs', 'lmfdb_label': '4650.bs2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -12585, -582075], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.j.1', '30.6.0.a.1', '40.6.0.c.1', '120.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 15], [3, 4, 775], [5, 14, 186], [7, 2, 1550], [31, 32, 150]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.88129923714939639686768571458', 'prec': 103}, 'szpiro_ratio': 5.886631711762168, '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, 1, 1, 0, 1, 2, 1, 1, 0, -6, 1, -2, 2, 0, 1, 6, 1, 8, 0], 'aplist': [1, 1, 0, 2, -6, -2, 6, 8, 4, -4, -1, 2, 2, -4, 8, 10, 6, -14, 4, 16, -8, 0, -4, 10, 16], 'class_deg': 2, 'class_size': 2, 'conductor': 4650, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4650.bs', 'trace_hash': 1015777768570752877}
• 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': '0.015348226594134315804594444446', 'prec': 107}, 'conductor': 4650, 'gens': [], 'heights': [], 'lmfdb_label': '4650.bs2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10036675126676938552559642167', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2154035532043141920750497100965156146', 'prec': 130}, 'tamagawa_product': 168, 'torsion_generators': [[652, -326, 1]], 'xcoord_integral_points': [652]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 0], '3': [3, 0], '5': 'a', '7': [2, 0], '31': [0, 0]}, 'iwp0': 11, 'lmfdb_label': '4650.bs2'}
• ec_torsion_growth •

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

  
  
  • id: 242034
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '4650.bs2', 'torsion': [2, 2]}
  • id: 242035
    {'degree': 4, 'field': [16, -8, -1, -2, 1], 'lmfdb_label': '4650.bs2', 'torsion': [4]}
  • id: 242038
    {'degree': 8, 'field': [-300, 0, 275, 0, -60, 0, 0, 0, 1], 'lmfdb_label': '4650.bs2', 'torsion': [6]}
  • id: 242037
    {'degree': 8, 'field': [16, -16, 28, -40, 36, -20, 7, -2, 1], 'lmfdb_label': '4650.bs2', 'torsion': [2, 4]}
  • id: 242036
    {'degree': 8, 'field': [96, -192, 96, 24, -26, 2, 9, -4, 1], 'lmfdb_label': '4650.bs2', 'torsion': [2, 4]}
  • id: 242040
    {'degree': 16, 'field': [2601, 0, 24030, 0, 54793, 0, 45750, 0, -8796, 0, -1850, 0, 177, 0, 30, 0, 1], 'lmfdb_label': '4650.bs2', 'torsion': [2, 6]}
  • id: 242039
    {'degree': 16, 'field': [23097636, 0, 117671616, 0, -67959540, 0, 3397464, 0, 636429, 0, -10556, 0, -570, 0, 36, 0, 1], 'lmfdb_label': '4650.bs2', 'torsion': [8]}
• 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: 88827
    {'conductor': 4650, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '4650.bs2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 88828
    {'conductor': 4650, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '4650.bs2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 88829
    {'conductor': 4650, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4650.bs2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 88830
    {'conductor': 4650, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '4650.bs2', 'prime': 31, '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: 1694172
    {'adelic_gens': [[61, 4, 2, 9], [1, 4, 0, 1], [82, 1, 79, 0], [28, 1, 23, 0], [1, 0, 4, 1], [117, 4, 116, 5], [3, 4, 8, 11], [1, 2, 2, 5], [17, 106, 104, 15]], 'adelic_image': '120.12.0.?', 'conductor': 4650, 'lmfdb_label': '4650.bs2', 'prime': 0}
  • id: 23004
    {'conductor': 4650, 'elladic_image': '2.3.0.1', 'lmfdb_label': '4650.bs2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4650.bs does not appear in ec_padic