Elliptic curve data - 2736.s2

Formats: - HTML - YAML - JSON - 2025-05-24T07:10:32.836993

• 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': '2736t2', 'Cnumber': 2, 'abc_quality': 0.9072668607940285, 'absD': 9701462016, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 228, 'ainvs': [0, 0, 0, -939, 10010], 'analytic_rank': 0, 'bad_primes': [2, 3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 2736, 'degree': 1536, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.65087107241120140673680630932', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2], 'jinv': [30664297, 3249], 'lmfdb_iso': '2736.s', 'lmfdb_label': '2736.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -7, 5], 'min_quad_twist_disc': 12, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '12.24.0-12.b.1.1', '76.24.0.?', '228.48.0.?'], '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': '-0.59158225248279874837804843060', 'prec': 107}, 'szpiro_ratio': 4.062045072368696, '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, 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': '0.27205741651811419609213571433', 'prec': 103}, 'conductor': 2736, 'gens': [], 'heights': [], 'lmfdb_label': '2736.s2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2531991180917072968750460872', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5063982361834145937500921744069279075', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[13, 0, 1], [22, 0, 1]], 'xcoord_integral_points': [-35, 13, 22]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '2736.s2'}
• ec_torsion_growth •

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

  
  
  • id: 142837
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '2736.s2', 'torsion': [2, 4]}
  • id: 142839
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '2736.s2', 'torsion': [2, 4]}
  • id: 142838
    {'degree': 4, 'field': [361, 0, 19, 0, 1], 'lmfdb_label': '2736.s2', 'torsion': [2, 4]}
  • id: 142842
    {'degree': 8, 'field': [-27, 0, -39, 0, 18, 0, 0, 0, 1], 'lmfdb_label': '2736.s2', 'torsion': [2, 6]}
  • id: 142841
    {'degree': 8, 'field': [256, 0, -712, 0, 153, 0, -16, 0, 1], 'lmfdb_label': '2736.s2', 'torsion': [2, 8]}
  • id: 142840
    {'degree': 8, 'field': [625, 0, 225, 0, 56, 0, 9, 0, 1], 'lmfdb_label': '2736.s2', 'torsion': [4, 4]}
  • id: 142843
    {'degree': 16, 'field': [1, 0, 4, 0, 29, 0, -60, 0, 152, 0, -60, 0, 29, 0, 4, 0, 1], 'lmfdb_label': '2736.s2', 'torsion': [2, 8]}
  • id: 142844
    {'degree': 16, 'field': [4, 24, -16, -136, 548, -1212, 1916, -2388, 2425, -2040, 1420, -812, 378, -140, 40, -8, 1], 'lmfdb_label': '2736.s2', 'torsion': [2, 8]}
  • id: 142845
    {'degree': 16, 'field': [9, 0, -219, 0, -356, 0, -438, 0, 30, 0, 73, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '2736.s2', 'torsion': [2, 12]}
• 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: 48561
    {'conductor': 2736, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '2736.s2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 48562
    {'conductor': 2736, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '2736.s2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 48563
    {'conductor': 2736, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2736.s2', 'prime': 19, '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: 1681908
    {'adelic_gens': [[111, 224, 226, 225], [63, 2, 34, 227], [225, 4, 224, 5], [1, 4, 0, 1], [151, 226, 0, 227], [1, 0, 4, 1]], 'adelic_image': '228.48.0.?', 'conductor': 2736, 'lmfdb_label': '2736.s2', 'prime': 0}
  • id: 13772
    {'conductor': 2736, 'elladic_image': '4.12.0.1', 'lmfdb_label': '2736.s2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 2736.s does not appear in ec_padic