Elliptic curve data - 2304.o4

Formats: - HTML - YAML - JSON - 2024-09-12T05:02:11.639519

• 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': '2304f', 'Clabel': '2304f1', 'Cnumber': 1, 'abc_quality': 1.311101219926227, 'absD': 3359232, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 240, 'ainvs': [0, 0, 0, 6, -88], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 2304, 'degree': 256, 'elladic_images': ['8.6.0.5', '5.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.068409221203428861993528224773', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [64, 9], 'lmfdb_iso': '2304.o', 'lmfdb_label': '2304.o4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 1, 3], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '5B'], 'modm_images': ['2.3.0.a.1', '5.6.0.a.1', '8.6.0.a.1', '10.18.0.a.1', '12.6.0.f.1', '20.36.0.d.2', '24.12.0.e.1', '40.72.1.e.2', '60.72.1.dx.2', '80.144.1.?', '120.144.5.?', '240.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 8, 256]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1375757509574426897540749343', 'prec': 103}, 'szpiro_ratio': 2.90321002490296, '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, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, 2, 2, 0, -4, 2, 4, 4, 6, 2, -8, 2, 4, 12, 6, 4, 0, -12, 12, 6, 10, -16, -10, -2], 'class_deg': 10, 'class_size': 4, 'conductor': 2304, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '2304.o', 'trace_hash': 866697413302317559}
• 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': '1.1466199520624008272351687786', 'prec': 100}, 'conductor': 2304, 'gens': [], 'heights': [], 'lmfdb_label': '2304.o4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1869637097891439356122242537', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3739274195782878712244485074645880755', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[4, 0, 1]], 'xcoord_integral_points': [4]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0]}, 'iwp0': 7, 'lmfdb_label': '2304.o4'}
• ec_torsion_growth •

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

  
  
  • id: 116675
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [2, 2]}
  • id: 116676
    {'degree': 4, 'field': [-2, 0, -4, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [4]}
  • id: 116677
    {'degree': 4, 'field': [18, 0, 12, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [10]}
  • id: 116680
    {'degree': 8, 'field': [-12, 0, 24, 0, -18, 0, 4, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [6]}
  • id: 116679
    {'degree': 8, 'field': [18, 0, 0, -24, 4, 0, 4, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [2, 4]}
  • id: 116678
    {'degree': 8, 'field': [36, 0, -24, 0, 10, 0, -4, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [2, 4]}
  • id: 116681
    {'degree': 8, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [2, 10]}
  • id: 116682
    {'degree': 16, 'field': [-72, 576, -2304, 6048, -11424, 16128, -17328, 14304, -9080, 4352, -1456, 224, 88, -80, 32, -8, 1], 'lmfdb_label': '2304.o4', 'torsion': [8]}
  • id: 116684
    {'degree': 16, 'field': [4, 0, 48, 0, 152, 0, 224, 0, 192, 0, 104, 0, 36, 0, 8, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [20]}
  • id: 116683
    {'degree': 16, 'field': [1089, 0, 2016, 0, 1764, 0, 1128, 0, 546, 0, 192, 0, 52, 0, 8, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [2, 6]}
  • id: 116685
    {'degree': 20, 'field': [1440, 0, 14400, 0, 31536, 0, -39744, 0, -3096, 0, 8112, 0, 4164, 0, 144, 0, -114, 0, -12, 0, 1], 'lmfdb_label': '2304.o4', 'torsion': [10]}
• 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: 38629
    {'conductor': 2304, 'conductor_valuation': 8, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '2304.o4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 38630
    {'conductor': 2304, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '2304.o4', 'prime': 3, 'reduction_type': 0, '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: 1678882
    {'adelic_gens': [[51, 20, 220, 107], [79, 220, 70, 39], [116, 225, 185, 146], [221, 20, 220, 21], [1, 20, 0, 1], [138, 5, 115, 82], [1, 0, 20, 1], [11, 16, 0, 131], [1, 10, 10, 101]], 'adelic_image': '240.288.5.?', 'conductor': 2304, 'lmfdb_label': '2304.o4', 'prime': 0}
  • id: 11295
    {'conductor': 2304, 'elladic_image': '8.6.0.5', 'lmfdb_label': '2304.o4', 'modell_image': '2B', 'prime': 2}
  • id: 11296
    {'conductor': 2304, 'elladic_image': '5.6.0.1', 'lmfdb_label': '2304.o4', 'modell_image': '5B', 'prime': 5}
• lmfdb_iso 2304.o does not appear in ec_padic