Elliptic curve data - 7872.p2

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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': '7872g', 'Clabel': '7872g2', 'Cnumber': 2, 'abc_quality': 0.9971398836095032, 'absD': 142775156736, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 328, 'ainvs': [0, -1, 0, -1857, -24255], 'analytic_rank': 0, 'bad_primes': [2, 3, 41], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 7872, 'degree': 9216, 'elladic_images': ['8.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.85628933173278676535267419998', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [2703045457, 544644], 'lmfdb_iso': '7872.p', 'lmfdb_label': '7872.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -29, -51], 'min_quad_twist_disc': 8, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '8.24.0-8.b.1.1', '164.24.0.?', '328.48.0.?'], '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, 1], [3, 4, 2624], [41, 42, 192]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.18343143910713119877317398221', 'prec': 107}, 'szpiro_ratio': 3.8116193423969205, '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, -1, 0, 2, 0, 4, 0, 1, 0, 4, 0, -2, 0, -2, 0, 2, 0, 4, 0], 'aplist': [0, -1, 2, 4, 4, -2, 2, 4, 0, 6, -8, 2, 1, -4, 12, 6, 4, 10, -12, -12, -6, 12, -12, 2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 7872, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '7872.p', 'trace_hash': 1361109262005375352}
• 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': '0.18040000142300246465641204201', 'prec': 103}, 'conductor': 7872, 'gens': [], 'heights': [], 'lmfdb_label': '7872.p2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.73750466638585975688910474532', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9500186655434390275564189812925721765', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-15, 0, 1], [49, 0, 1]], 'xcoord_integral_points': [-33, -15, 49]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '41': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '7872.p2'}
• ec_torsion_growth •

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

  
  
  • id: 411354
    {'degree': 2, 'field': [-82, 0, 1], 'lmfdb_label': '7872.p2', 'torsion': [2, 4]}
  • id: 411356
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '7872.p2', 'torsion': [2, 4]}
  • id: 411355
    {'degree': 4, 'field': [146, 16, -15, -2, 1], 'lmfdb_label': '7872.p2', 'torsion': [2, 4]}
  • id: 411359
    {'degree': 8, 'field': [-768, 0, -800, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '7872.p2', 'torsion': [2, 6]}
  • id: 411358
    {'degree': 8, 'field': [256, 0, -256, 0, -232, 0, -16, 0, 1], 'lmfdb_label': '7872.p2', 'torsion': [2, 8]}
  • id: 411357
    {'degree': 8, 'field': [10000, 0, 0, 0, 241, 0, 0, 0, 1], 'lmfdb_label': '7872.p2', 'torsion': [4, 4]}
  • id: 411361
    {'degree': 16, 'field': [16, 0, 160, 0, 416, 0, 120, 0, 401, 0, -60, 0, 104, 0, -20, 0, 1], 'lmfdb_label': '7872.p2', 'torsion': [2, 8]}
  • id: 411360
    {'degree': 16, 'field': [118336, 0, 284736, 0, -358736, 0, 23040, 0, 65292, 0, 14580, 0, 1429, 0, 66, 0, 1], 'lmfdb_label': '7872.p2', 'torsion': [2, 8]}
  • id: 411362
    {'degree': 16, 'field': [1220527888, 102364000, -131819304, 59092056, -30015420, 607428, -276527, 65848, -22722, 9270, -6903, 2676, -355, -70, 30, -8, 1], 'lmfdb_label': '7872.p2', '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: 162653
    {'conductor': 7872, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '7872.p2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 162654
    {'conductor': 7872, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '7872.p2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 162655
    {'conductor': 7872, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '7872.p2', 'prime': 41, '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: 1715947
    {'adelic_gens': [[1, 0, 4, 1], [325, 4, 324, 5], [1, 4, 0, 1], [161, 326, 2, 1], [129, 2, 0, 1], [247, 4, 166, 9]], 'adelic_image': '328.48.0.?', 'conductor': 7872, 'lmfdb_label': '7872.p2', 'prime': 0}
  • id: 38484
    {'conductor': 7872, 'elladic_image': '8.24.0.3', 'lmfdb_label': '7872.p2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 7872.p does not appear in ec_padic