Elliptic curve data - 47040.ha4

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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': '47040dm', 'Clabel': '47040dm4', 'Cnumber': 4, 'abc_quality': 1.0358020223701003, 'absD': 3717288506425658572800, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [0, 1, 0, -47259585, -125031134817], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 47040, 'degree': 4718592, 'elladic_images': ['16.96.0.241'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1139580817031923542143306799', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 182, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [378499465220294881, 120530818800], 'lmfdb_iso': '47040.ha', 'lmfdb_label': '47040.ha4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -15070, 710612], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0-8.bb.1.4', '16.96.0-16.v.1.7', '28.12.0.h.1', '56.96.0-56.bl.2.4', '80.192.2.?', '96.192.1.?', '112.192.1.?', '480.384.5.?', '560.384.5.?', '672.384.5.?', '3360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 15680], [5, 6, 9408], [7, 32, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1012822363356177375358061260', 'prec': 100}, 'szpiro_ratio': 6.0069320022341275, '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, 1, 0, 0, 0, 1, 0, 4, 0, -2, 0, 1, 0, -2, 0, 4, 0], 'aplist': [0, 1, 1, 0, 4, -2, -2, 4, -8, 2, 0, -6, 6, 4, 0, 10, 12, 14, 12, -8, -10, 16, -12, -10, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 47040, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '47040.ha', 'trace_hash': 1026332402822852115}
• 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': '0.0019735601915923187284604361927', 'prec': 110}, 'conductor': 47040, 'gens': [], 'heights': [], 'lmfdb_label': '47040.ha4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.057581818672342353255199044297', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6852363950299106083327388349882004548', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[-4023, 0, 1]], 'xcoord_integral_points': [-4023]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [5, 0], '5': [1, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '47040.ha4'}
• ec_torsion_growth •

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

  
  
  • id: 2294544
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [2, 2]}
  • id: 2294545
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [4]}
  • id: 2294546
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [8]}
  • id: 2294547
    {'degree': 4, 'field': [9, 0, 8, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [2, 8]}
  • id: 2294548
    {'degree': 4, 'field': [36, 0, 2, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [16]}
  • id: 2294549
    {'degree': 4, 'field': [81, 0, 38, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [16]}
  • id: 2294553
    {'degree': 8, 'field': [-588, 0, 4382, 0, 84, 0, 0, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [6]}
  • id: 2294550
    {'degree': 8, 'field': [36, 0, -116, 0, -43, 0, -4, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [2, 4]}
  • id: 2294552
    {'degree': 8, 'field': [225, 0, -190, 0, 39, 0, 6, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [2, 16]}
  • id: 2294551
    {'degree': 8, 'field': [1936, 0, -262, 0, 89, 0, 2, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [8]}
  • id: 2294556
    {'degree': 16, 'field': [16, 0, 0, 0, -24, 0, 0, 0, 73, 0, 0, 0, 15, 0, 0, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [2, 16]}
  • id: 2294555
    {'degree': 16, 'field': [25281, 0, -79424, 0, -96208, 0, -21392, 0, 770, 0, -448, 0, 112, 0, -16, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [2, 8]}
  • id: 2294554
    {'degree': 16, 'field': [87616, 0, -63424, 0, 42772, 0, -11940, 0, 3561, 0, -360, 0, 22, 0, -4, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [4, 8]}
  • id: 2294557
    {'degree': 16, 'field': [2250000, 0, -600000, 0, 46000, 0, -12000, 0, 87900, 0, 5200, 0, 1740, 0, 0, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [32]}
  • id: 2294560
    {'degree': 16, 'field': [42055225, 0, -3470288, 0, 4164580, 0, 675724, 0, 76762, 0, -560, 0, -560, 0, 4, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [12]}
  • id: 2294561
    {'degree': 16, 'field': [64577296, 0, -45542168, 0, 482356, 0, 3664024, 0, 247156, 0, 5236, 0, -224, 0, 28, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [24]}
  • id: 2294559
    {'degree': 16, 'field': [2057801769, 0, -133536864, 0, -63680804, 0, 2183232, 0, 441534, 0, -9056, 0, -1524, 0, 0, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [2, 6]}
  • id: 2294558
    {'degree': 16, 'field': [178611890625, 0, -64466850000, 0, 7306243000, 0, -288120000, 0, 8900850, 0, -98000, 0, 5880, 0, 0, 0, 1], 'lmfdb_label': '47040.ha4', 'torsion': [32]}
• 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: 1122662
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '47040.ha4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1122663
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '47040.ha4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 1122664
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '47040.ha4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1122665
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '47040.ha4', 'prime': 7, 'reduction_type': 0, '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: 1977708
    {'adelic_gens': [[1121, 32, 1136, 513], [1, 0, 32, 1], [242, 19, 975, 2318], [1, 32, 0, 1], [5, 28, 68, 381], [1239, 3328, 1556, 451], [2711, 26, 2118, 875], [2368, 3331, 2453, 798], [3329, 32, 3328, 33], [23, 18, 798, 1355]], 'adelic_image': '3360.768.13.?', 'conductor': 47040, 'lmfdb_label': '47040.ha4', 'prime': 0}
  • id: 203641
    {'conductor': 47040, 'elladic_image': '16.96.0.241', 'lmfdb_label': '47040.ha4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 47040.ha does not appear in ec_padic