Elliptic curve data - 6720.bg4

Formats: - HTML - YAML - JSON - 2023-03-28T20:19:29.876216

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '6720bu', 'Clabel': '6720bu4', 'Cnumber': 4, 'absD': 28689339248640000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, -1, 0, -69665, 10816737], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6720, 'degree': 61440, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8568306276406323782126975014', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4], 'jinv': [-1141100604753992, 875529151875], 'lmfdb_iso': '6720.bg', 'lmfdb_label': '6720.bg4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -17416, 1343384], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['1.1.0.1', '2.3.0.1', '4.12.0.7', '24.24.0.49', '40.24.0.47', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.99039665194070074144115734958', 'prec': 103}, '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, -1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 6, 0, -1, 0, 6, 0, 0, 0], 'aplist': [0, -1, 1, 1, 4, 6, 6, 0, 4, 6, 0, -2, 2, 4, -4, 6, 12, 10, 4, -8, -14, -8, -12, -6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 6720, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '6720.bg', 'trace_hash': 1396786929471627832}
• 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': '0.024388068668298193575730919752', 'prec': 107}, 'conductor': 6720, 'gens': [], 'heights': [], 'lmfdb_label': '6720.bg4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.34297785141915502818549986776', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7438228113532402254839989420555875767', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[169, 1960, 1]], 'xcoord_integral_points': [-321, 169]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [1, 0], '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '6720.bg4'}
• ec_torsion_growth •

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

  
  
  • id: 353006
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '6720.bg4', 'torsion': [2, 4]}
  • id: 353007
    {'degree': 4, 'field': [-24, 0, -8, 0, 1], 'lmfdb_label': '6720.bg4', 'torsion': [8]}
  • id: 353011
    {'degree': 8, 'field': [-3, 0, -1952, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '6720.bg4', 'torsion': [12]}
  • id: 353008
    {'degree': 8, 'field': [25, 0, 76, 0, -6, 0, 4, 0, 1], 'lmfdb_label': '6720.bg4', 'torsion': [4, 4]}
  • id: 353009
    {'degree': 8, 'field': [490, 320, 124, 176, 118, 8, -8, -4, 1], 'lmfdb_label': '6720.bg4', 'torsion': [2, 8]}
  • id: 353010
    {'degree': 8, 'field': [1296, 0, 720, 0, 178, 0, 20, 0, 1], 'lmfdb_label': '6720.bg4', 'torsion': [2, 8]}
  • id: 353012
    {'degree': 16, 'field': [51969681, 0, 303503112, 0, -29734452, 0, -10670616, 0, 1214010, 0, -63096, 0, 2948, 0, -88, 0, 1], 'lmfdb_label': '6720.bg4', 'torsion': [16]}
  • id: 353013
    {'degree': 16, 'field': [163558521, 0, -18390288, 0, -6291404, 0, 2500944, 0, 402606, 0, 8336, 0, 996, 0, 48, 0, 1], 'lmfdb_label': '6720.bg4', '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: 136770
    {'conductor': 6720, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '6720.bg4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 136771
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '6720.bg4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 136772
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6720.bg4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 136773
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '6720.bg4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

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

  
  
  • id: 1708214
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [49, 48, 118, 55], [88, 3, 85, 2], [113, 8, 112, 9], [72, 7, 53, 66], [7, 6, 114, 115], [97, 8, 28, 33], [1, 4, 4, 17]], 'adelic_image': '120.48.0.?', 'conductor': 6720, 'lmfdb_label': '6720.bg4', 'prime': 0}
  • id: 33074
    {'conductor': 6720, 'elladic_image': '4.12.0.7', 'lmfdb_label': '6720.bg4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6720.bg does not appear in ec_padic