Elliptic curve data - 2736.s4

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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': '2736t', 'Clabel': '2736t4', 'Cnumber': 4, 'abc_quality': 0.9747386105988611, 'absD': 1167409262592, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, 0, 0, 1221, 49322], 'analytic_rank': 0, 'bad_primes': [2, 3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 2736, 'degree': 3072, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.99744466269117406144542237005', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2, 4], 'jinv': [67419143, 390963], 'lmfdb_iso': '2736.s', 'lmfdb_label': '2736.s4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 8, 29], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '6.6.0.a.1', '12.24.0-12.g.1.2', '152.24.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 304], [19, 20, 144]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.24500866220282609366943236987', 'prec': 107}, 'szpiro_ratio': 4.439509294882377, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 0, 0, 6, 0, 0, 0, 6, 0, 1, 0], 'aplist': [0, 0, 2, 0, 0, 6, 6, 1, 4, -2, -8, -10, 2, 4, 12, 6, -12, -2, 4, 0, 10, 0, 16, 2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 2736, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '2736.s', 'trace_hash': 1543816632100312673}
• 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': '0.13602870825905709804606785717', 'prec': 103}, 'conductor': 2736, 'gens': [], 'heights': [], 'lmfdb_label': '2736.s4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.62659955904585364843752304360', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5063982361834145937500921744069279075', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[31, 342, 1]], 'xcoord_integral_points': [-26, 31]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '2736.s4'}
• ec_torsion_growth •

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

  
  
  • id: 142861
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '2736.s4', 'torsion': [2, 4]}
  • id: 142862
    {'degree': 4, 'field': [-48, 0, 6, 0, 1], 'lmfdb_label': '2736.s4', 'torsion': [8]}
  • id: 142866
    {'degree': 8, 'field': [-27, 0, -39, 0, 18, 0, 0, 0, 1], 'lmfdb_label': '2736.s4', 'torsion': [12]}
  • id: 142863
    {'degree': 8, 'field': [1, -4, 8, -10, 7, -2, 2, -2, 1], 'lmfdb_label': '2736.s4', 'torsion': [4, 4]}
  • id: 142864
    {'degree': 8, 'field': [9, 0, -24, 0, 67, 0, 8, 0, 1], 'lmfdb_label': '2736.s4', 'torsion': [2, 8]}
  • id: 142865
    {'degree': 8, 'field': [2304, 0, 288, 0, 84, 0, -6, 0, 1], 'lmfdb_label': '2736.s4', 'torsion': [2, 8]}
  • id: 142868
    {'degree': 16, 'field': [9, 0, -33, 0, 103, 0, -66, 0, 39, 0, -22, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '2736.s4', 'torsion': [2, 12]}
  • id: 142867
    {'degree': 16, 'field': [831744, 0, -831744, 0, 191520, 0, -10944, 0, 480, 0, 336, 0, -174, 0, 12, 0, 1], 'lmfdb_label': '2736.s4', 'torsion': [16]}
• 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: 48567
    {'conductor': 2736, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '2736.s4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 48568
    {'conductor': 2736, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '2736.s4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 48569
    {'conductor': 2736, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '2736.s4', 'prime': 19, 'reduction_type': 1, '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: 1681910
    {'adelic_gens': [[277, 284, 238, 51], [7, 6, 450, 451], [97, 8, 388, 33], [1, 0, 8, 1], [296, 453, 299, 454], [449, 8, 448, 9], [403, 402, 298, 67], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '456.48.0.?', 'conductor': 2736, 'lmfdb_label': '2736.s4', 'prime': 0}
  • id: 13774
    {'conductor': 2736, 'elladic_image': '4.12.0.7', 'lmfdb_label': '2736.s4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 2736.s does not appear in ec_padic