Elliptic curve data - 4416.f1

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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': '4416c', 'Clabel': '4416c2', 'Cnumber': 2, 'abc_quality': 0.9246304097924353, 'absD': 416022528, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 276, 'ainvs': [0, -1, 0, -993, -11679], 'analytic_rank': 1, 'bad_primes': [2, 3, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4416, 'degree': 2048, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.51232722256824887020483372649', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [413493625, 1587], 'lmfdb_iso': '4416.f', 'lmfdb_label': '4416.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -16, -25], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '92.6.0.?', '276.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.4789331055068649675729720595', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 4, 1472], [23, 24, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.52739354827166909392101445570', 'prec': 107}, 'szpiro_ratio': 3.8504518046333516, '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, -1, 0, 0, 0, -2, 0, 1, 0, -4, 0, 6, 0, 0, 0, 4, 0, -2, 0], 'aplist': [0, -1, 0, -2, -4, 6, 4, -2, -1, -2, 4, -2, 2, -10, 0, 12, 12, 6, 10, 8, -14, 10, -12, -16, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 4416, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4416.f', 'trace_hash': 316390604555953434}
• 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': '0.35892047069366123775816084988', 'prec': 103}, 'conductor': 4416, 'gens': [[47, 208, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.4789331055068649675729720595', 'prec': 100}], 'lmfdb_label': '4416.f1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.85060132768203467103942972489', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9591851184611233452099383147762428106', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-17, 0, 1]], 'xcoord_integral_points': [-17, 47]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [3, 1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '4416.f1'}
• ec_torsion_growth •

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

  
  
  • id: 230740
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '4416.f1', 'torsion': [2, 2]}
  • id: 230741
    {'degree': 4, 'field': [48, 0, -10, 0, 1], 'lmfdb_label': '4416.f1', 'torsion': [4]}
  • id: 230744
    {'degree': 8, 'field': [-1200, 0, 2008, 0, 120, 0, 0, 0, 1], 'lmfdb_label': '4416.f1', 'torsion': [6]}
  • id: 230742
    {'degree': 8, 'field': [88, 304, 296, 256, -8, -16, -4, -4, 1], 'lmfdb_label': '4416.f1', 'torsion': [2, 4]}
  • id: 230743
    {'degree': 8, 'field': [676, 0, 116, 0, 45, 0, 8, 0, 1], 'lmfdb_label': '4416.f1', 'torsion': [2, 4]}
  • id: 230745
    {'degree': 16, 'field': [324, 0, 7830, 0, 69957, 0, 57390, 0, 24400, 0, 4960, 0, 632, 0, 40, 0, 1], 'lmfdb_label': '4416.f1', 'torsion': [8]}
  • id: 230746
    {'degree': 16, 'field': [729, 0, 4212, 0, 8325, 0, 2808, 0, -4914, 0, -2028, 0, -252, 0, 0, 0, 1], 'lmfdb_label': '4416.f1', 'torsion': [2, 6]}
• 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: 83859
    {'conductor': 4416, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '4416.f1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 83860
    {'conductor': 4416, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4416.f1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 83861
    {'conductor': 4416, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4416.f1', 'prime': 23, '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: 1692741
    {'adelic_gens': [[1, 2, 2, 5], [1, 4, 0, 1], [97, 4, 194, 9], [273, 4, 272, 5], [208, 73, 69, 208], [1, 0, 4, 1], [3, 4, 8, 11], [94, 1, 91, 0]], 'adelic_image': '276.12.0.?', 'conductor': 4416, 'lmfdb_label': '4416.f1', 'prime': 0}
  • id: 21999
    {'conductor': 4416, 'elladic_image': '2.3.0.1', 'lmfdb_label': '4416.f1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 157382
    {'lmfdb_iso': '4416.f', 'p': 7, 'prec': 20, 'unit': 9595327795221229, 'val': 1}
  • id: 157388
    {'lmfdb_iso': '4416.f', 'p': 11, 'prec': 20, 'unit': 54344115363071241908, 'val': 1}
  • id: 157386
    {'lmfdb_iso': '4416.f', 'p': 13, 'prec': 20, 'unit': 907202037461320012375, 'val': 1}
  • id: 157389
    {'lmfdb_iso': '4416.f', 'p': 17, 'prec': 20, 'unit': 23233334284945994147258, 'val': 1}
  • id: 157390
    {'lmfdb_iso': '4416.f', 'p': 19, 'prec': 20, 'unit': 257080331842244192829294, 'val': 1}
  • id: 157385
    {'lmfdb_iso': '4416.f', 'p': 29, 'prec': 20, 'unit': 78223633286824162300650538, 'val': 1}
  • id: 157397
    {'lmfdb_iso': '4416.f', 'p': 31, 'prec': 20, 'unit': 21130162897057646449645635344, 'val': 1}
  • id: 157381
    {'lmfdb_iso': '4416.f', 'p': 37, 'prec': 20, 'unit': 293237416036588519818681335863, 'val': 1}
  • id: 157383
    {'lmfdb_iso': '4416.f', 'p': 41, 'prec': 20, 'unit': 4172246279004955766243091068292, 'val': 1}
  • id: 157384
    {'lmfdb_iso': '4416.f', 'p': 43, 'prec': 20, 'unit': 8562173727433212929570694722656, 'val': 1}
  • id: 157391
    {'lmfdb_iso': '4416.f', 'p': 53, 'prec': 20, 'unit': 524922455539080635861337720431753, 'val': 1}
  • id: 157395
    {'lmfdb_iso': '4416.f', 'p': 59, 'prec': 20, 'unit': 3584746411449374095094606365792027, 'val': 1}
  • id: 157396
    {'lmfdb_iso': '4416.f', 'p': 61, 'prec': 20, 'unit': 3422551657106904629660442461755369, 'val': 1}
  • id: 157380
    {'lmfdb_iso': '4416.f', 'p': 67, 'prec': 20, 'unit': 20020507820680207663009750146183959, 'val': 1}
  • id: 157394
    {'lmfdb_iso': '4416.f', 'p': 71, 'prec': 20, 'unit': 109561115342255349613855538935779243, 'val': 1}
  • id: 157392
    {'lmfdb_iso': '4416.f', 'p': 73, 'prec': 20, 'unit': 184386810147559791875328991561073723, 'val': 1}
  • id: 157387
    {'lmfdb_iso': '4416.f', 'p': 79, 'prec': 20, 'unit': 830950142562541078624567351346894588, 'val': 1}
  • id: 157379
    {'lmfdb_iso': '4416.f', 'p': 83, 'prec': 20, 'unit': 1617292781878691746518043263825971594, 'val': 1}
  • id: 157393
    {'lmfdb_iso': '4416.f', 'p': 89, 'prec': 20, 'unit': 8885653377864458041529161630251804412, 'val': 1}
  • id: 157378
    {'lmfdb_iso': '4416.f', 'p': 97, 'prec': 20, 'unit': 21776867786466861886714556722073102639, 'val': 1}