Elliptic curve data - 27720.u4

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '27720k', 'Clabel': '27720k2', 'Cnumber': 2, 'abc_quality': 0.9464004009656585, 'absD': 222328469895840000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1848, 'ainvs': [0, 0, 0, -274503, -50494502], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 27720, 'degree': 262144, 'elladic_images': ['8.24.0.18'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0658046154466258863350113986', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2, 4], 'jinv': [12257375872392016, 1191317675625], 'lmfdb_iso': '27720.u', 'lmfdb_label': '27720.u4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -30500, 1860000], 'min_quad_twist_disc': -3, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.1', '12.24.0-4.b.1.3', '24.48.0-8.e.1.9', '44.24.0.c.1', '56.48.0.q.1', '88.48.0.?', '132.48.0.?', '168.96.0.?', '264.96.0.?', '616.96.1.?', '1848.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, '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': '1.0544003507392741676925673658', 'prec': 100}, 'szpiro_ratio': 4.807643280101686, '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, -1, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 6, 0, -4, 0], 'aplist': [0, 0, -1, 1, 1, -2, 6, -4, 0, -6, 0, -10, -2, 4, 0, -6, 4, -2, -4, 16, 2, 0, -12, 6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 27720, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '27720.u', 'trace_hash': 1343273755827159326}
• 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': '0.016057018570273857006713428919', 'prec': 107}, 'conductor': 27720, 'gens': [], 'heights': [], 'lmfdb_label': '27720.u4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20987823150178723895052734377', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6790258520142979116042187501805275922', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-226, 0, 1], [599, 0, 1]], 'xcoord_integral_points': [-373, -226, 599]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': [1, 0], '11': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '27720.u4'}
• ec_torsion_growth •

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

  
  
  • id: 1386489
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '27720.u4', 'torsion': [2, 4]}
  • id: 1386490
    {'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '27720.u4', 'torsion': [2, 4]}
  • id: 1386491
    {'degree': 4, 'field': [33, 0, 1, -2, 1], 'lmfdb_label': '27720.u4', 'torsion': [2, 4]}
  • id: 1386496
    {'degree': 8, 'field': [-1594323, 0, -109836, 0, -4374, 0, 0, 0, 1], 'lmfdb_label': '27720.u4', 'torsion': [2, 6]}
  • id: 1386492
    {'degree': 8, 'field': [81, 0, 45, 0, 16, 0, 5, 0, 1], 'lmfdb_label': '27720.u4', 'torsion': [4, 4]}
  • id: 1386494
    {'degree': 8, 'field': [81, 0, 72, 0, 55, 0, 8, 0, 1], 'lmfdb_label': '27720.u4', 'torsion': [2, 8]}
  • id: 1386493
    {'degree': 8, 'field': [4486, 688, -824, 274, -141, 2, 4, -4, 1], 'lmfdb_label': '27720.u4', 'torsion': [2, 8]}
  • id: 1386495
    {'degree': 8, 'field': [6561, 0, 324, 0, -65, 0, 4, 0, 1], 'lmfdb_label': '27720.u4', 'torsion': [2, 8]}
  • id: 1386498
    {'degree': 16, 'field': [22667121, -657018, 9522, -2571216, 651433, -82674, 147954, -54938, 15668, -3176, 2216, -842, 153, -12, 8, -4, 1], 'lmfdb_label': '27720.u4', 'torsion': [4, 8]}
  • id: 1386497
    {'degree': 16, 'field': [266048721, 0, 10159032, 0, 13199290, 0, 38012, 0, 217959, 0, -5252, 0, 1290, 0, -52, 0, 1], 'lmfdb_label': '27720.u4', 'torsion': [2, 8]}
  • id: 1386499
    {'degree': 16, 'field': [387420489, 0, 80070444, 0, 6982686, 0, 1977048, 0, 255879, 0, 8136, 0, 486, 0, 0, 0, 1], 'lmfdb_label': '27720.u4', '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: 639935
    {'conductor': 27720, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '27720.u4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 639936
    {'conductor': 27720, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '27720.u4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 639937
    {'conductor': 27720, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '27720.u4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 639938
    {'conductor': 27720, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '27720.u4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 639939
    {'conductor': 27720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '27720.u4', 'prime': 11, '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: 1848886
    {'adelic_gens': [[313, 156, 156, 925], [1015, 6, 1506, 1843], [1841, 8, 1840, 9], [1, 0, 8, 1], [5, 4, 1844, 1845], [619, 1698, 624, 781], [1585, 624, 180, 649], [1, 8, 0, 1], [1231, 0, 0, 1847]], 'adelic_image': '1848.192.1.?', 'conductor': 27720, 'lmfdb_label': '27720.u4', 'prime': 0}
  • id: 125336
    {'conductor': 27720, 'elladic_image': '8.24.0.18', 'lmfdb_label': '27720.u4', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 27720.u does not appear in ec_padic