Elliptic curve data - 48960.v2

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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': '48960bn', 'Clabel': '48960bn1', 'Cnumber': 1, 'abc_quality': 0.9201382831476481, 'absD': 97418894400, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2040, 'ainvs': [0, 0, 0, -4323, -110428], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 48960, 'degree': 36864, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.92412064816448229868193042422', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2], 'jinv': [-191501383744, 2088025], 'lmfdb_iso': '48960.v', 'lmfdb_label': '48960.v2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1921, 32079], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '12.12.0-4.a.1.1', '20.12.0.d.1', '60.24.0-20.d.1.1', '680.24.0.?', '2040.48.0.?'], '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, 2, 9], [3, 6, 5440], [5, 6, 9792], [17, 18, 2880]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.028240913550454798275691745030', 'prec': 107}, 'szpiro_ratio': 3.4029265610178534, '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, -1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0], 'aplist': [0, 0, -1, -2, 0, -2, -1, 0, -2, 6, -8, -10, 2, -2, 6, 2, -8, -2, 2, -8, 2, -4, -6, 6, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 48960, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '48960.v', 'trace_hash': 253805738353434124}
• 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': '0.15751394320817671663749036196', 'prec': 103}, 'conductor': 48960, 'gens': [], 'heights': [], 'lmfdb_label': '48960.v2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29419891897872771437881739483', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.58839783795745542875763478966412650308', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[76, 0, 1]], 'xcoord_integral_points': [76]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '48960.v2'}
• ec_torsion_growth •

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

  
  
  • id: 2382648
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [2, 2]}
  • id: 2382649
    {'degree': 4, 'field': [-36, 0, -6, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [4]}
  • id: 2382652
    {'degree': 8, 'field': [-75, 0, 0, 0, -30, 0, 16, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [6]}
  • id: 2382650
    {'degree': 8, 'field': [25, 0, -20, 0, 11, 0, -4, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [2, 4]}
  • id: 2382651
    {'degree': 8, 'field': [81, 0, 0, 0, 27, 0, 0, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [2, 4]}
  • id: 2382653
    {'degree': 16, 'field': [1, 0, 0, 0, -3, 0, 0, 0, 8, 0, 0, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [4, 4]}
  • id: 2382655
    {'degree': 16, 'field': [90000, 0, -13824, 0, 86472, 0, -41328, 0, 12405, 0, -2280, 0, 298, 0, -24, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [2, 6]}
  • id: 2382654
    {'degree': 16, 'field': [923521, 0, 24103356, 0, -21434530, 0, 6381704, 0, -693261, 0, 17864, 0, -930, 0, -4, 0, 1], 'lmfdb_label': '48960.v2', '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: 1170317
    {'conductor': 48960, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '48960.v2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1170318
    {'conductor': 48960, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48960.v2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1170319
    {'conductor': 48960, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '48960.v2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1170320
    {'conductor': 48960, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '48960.v2', 'prime': 17, '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: 1990256
    {'adelic_gens': [[1019, 1356, 678, 671], [3, 8, 10, 27], [1, 0, 8, 1], [817, 1362, 0, 1], [1, 8, 0, 1], [5, 8, 48, 77], [679, 0, 0, 2039], [2033, 8, 2032, 9], [241, 684, 0, 1], [509, 1356, 255, 2039]], 'adelic_image': '2040.48.0.?', 'conductor': 48960, 'lmfdb_label': '48960.v2', 'prime': 0}
  • id: 211153
    {'conductor': 48960, 'elladic_image': '4.6.0.5', 'lmfdb_label': '48960.v2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 48960.v does not appear in ec_padic