Elliptic curve data - 3648.w4

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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': '3648bg', 'Clabel': '3648bg4', 'Cnumber': 4, 'abc_quality': 0.9864610024765296, 'absD': 1323483660288, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, 1, 0, 2271, 37215], 'analytic_rank': 1, 'bad_primes': [2, 3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3648, 'degree': 3072, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0127759291431659994196579360', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 22, 'isogeny_degrees': [1, 2, 4], 'jinv': [9878111854, 10097379], 'lmfdb_iso': '3648.w', 'lmfdb_label': '3648.w4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 568, -4368], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '24.24.0-24.y.1.4', '152.24.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.1961376963824128740594846076', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 19], [3, 4, 1216], [19, 20, 192]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.030817423349910144411912430602', 'prec': 107}, 'szpiro_ratio': 4.242546672785858, '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, -2, 0, 0, 0, 1, 0, 0, 0, -2, 0, -2, 0, 2, 0, -1, 0], 'aplist': [0, 1, -2, 0, 0, -2, 2, -1, 0, -2, 4, -2, 6, -4, 0, -10, -4, 2, -12, 0, -6, 4, -8, 6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 3648, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '3648.w', 'trace_hash': 965382551901016951}
• 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': '0.13192102138722738487487426366', 'prec': 103}, 'conductor': 3648, 'gens': [[-6, 153, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.1961376963824128740594846076', 'prec': 100}], 'lmfdb_label': '3648.w4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.56633801582725253859694564332', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.7312687963579466173382784095816105916', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[39, 432, 1]], 'xcoord_integral_points': [-15, -6, 39, 135, 309]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [3, 1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [3, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '3648.w4'}
• ec_torsion_growth •

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

  
  
  • id: 190842
    {'degree': 2, 'field': [38, 0, 1], 'lmfdb_label': '3648.w4', 'torsion': [2, 4]}
  • id: 190843
    {'degree': 4, 'field': [-38, 0, -8, 0, 1], 'lmfdb_label': '3648.w4', 'torsion': [8]}
  • id: 190847
    {'degree': 8, 'field': [-3, 0, -46, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '3648.w4', 'torsion': [12]}
  • id: 190844
    {'degree': 8, 'field': [1521, 0, -452, 0, 82, 0, 4, 0, 1], 'lmfdb_label': '3648.w4', 'torsion': [4, 4]}
  • id: 190845
    {'degree': 8, 'field': [5184, 0, 8784, 0, -527, 0, -8, 0, 1], 'lmfdb_label': '3648.w4', 'torsion': [2, 8]}
  • id: 190846
    {'degree': 8, 'field': [7569, 0, -1020, 0, 64, 0, 4, 0, 1], 'lmfdb_label': '3648.w4', 'torsion': [2, 8]}
  • id: 190849
    {'degree': 16, 'field': [112842, -102672, 244548, -332640, 378642, -346092, 249332, -141052, 65436, -16312, -718, 1476, -296, -8, 24, -8, 1], 'lmfdb_label': '3648.w4', 'torsion': [2, 12]}
  • id: 190848
    {'degree': 16, 'field': [2085136, 0, 1755904, 0, -912608, 0, 300352, 0, 23104, 0, -7904, 0, -632, 0, -32, 0, 1], 'lmfdb_label': '3648.w4', 'torsion': [16]}
• 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: 67334
    {'conductor': 3648, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '3648.w4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 67335
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '3648.w4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 67336
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3648.w4', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1687714
    {'adelic_gens': [[449, 8, 448, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 450, 451], [168, 391, 293, 306], [320, 3, 29, 2], [277, 284, 238, 51], [305, 8, 308, 33]], 'adelic_image': '456.48.0.?', 'conductor': 3648, 'lmfdb_label': '3648.w4', 'prime': 0}
  • id: 18290
    {'conductor': 3648, 'elladic_image': '4.12.0.7', 'lmfdb_label': '3648.w4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 123858
    {'lmfdb_iso': '3648.w', 'p': 5, 'prec': 20, 'unit': 3812065192861, 'val': 1}
  • id: 123849
    {'lmfdb_iso': '3648.w', 'p': 13, 'prec': 20, 'unit': 397854817945966058711, 'val': 1}
  • id: 123851
    {'lmfdb_iso': '3648.w', 'p': 17, 'prec': 20, 'unit': 184662160565250209646106, 'val': 1}
  • id: 123848
    {'lmfdb_iso': '3648.w', 'p': 29, 'prec': 20, 'unit': 1519920978862040844209672164, 'val': 1}
  • id: 123845
    {'lmfdb_iso': '3648.w', 'p': 31, 'prec': 20, 'unit': 915453931547003263715395758, 'val': 1}
  • id: 123844
    {'lmfdb_iso': '3648.w', 'p': 37, 'prec': 20, 'unit': 571980622441229241594984282, 'val': 1}
  • id: 123846
    {'lmfdb_iso': '3648.w', 'p': 41, 'prec': 20, 'unit': 2670579702814689091908780292458, 'val': 1}
  • id: 123847
    {'lmfdb_iso': '3648.w', 'p': 43, 'prec': 20, 'unit': 107513863616663890531309373687, 'val': 2}
  • id: 123853
    {'lmfdb_iso': '3648.w', 'p': 53, 'prec': 20, 'unit': 178431725585761900395832514282254, 'val': 1}
  • id: 123856
    {'lmfdb_iso': '3648.w', 'p': 59, 'prec': 20, 'unit': 1893729166517736349967714085561343, 'val': 1}
  • id: 123857
    {'lmfdb_iso': '3648.w', 'p': 61, 'prec': 20, 'unit': 24591983097164024697264750590234, 'val': 1}
  • id: 123843
    {'lmfdb_iso': '3648.w', 'p': 67, 'prec': 20, 'unit': 22569394059604450098348448523144598, 'val': 1}
  • id: 123854
    {'lmfdb_iso': '3648.w', 'p': 73, 'prec': 20, 'unit': 130984924661352058580804132404831761, 'val': 1}
  • id: 123850
    {'lmfdb_iso': '3648.w', 'p': 79, 'prec': 20, 'unit': 879024795450027080660281481843083253, 'val': 1}
  • id: 123852
    {'lmfdb_iso': '3648.w', 'p': 83, 'prec': 20, 'unit': 284560470819763760554254493908480826, 'val': 1}
  • id: 123855
    {'lmfdb_iso': '3648.w', 'p': 89, 'prec': 20, 'unit': 2113628674832104293570170114109883121, 'val': 1}
  • id: 123842
    {'lmfdb_iso': '3648.w', 'p': 97, 'prec': 20, 'unit': 15251780973223662838571762716649057101, 'val': 1}