Elliptic curve data - 7056.q4

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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': '7056z', 'Clabel': '7056z2', 'Cnumber': 2, 'abc_quality': 0.972547111469975, 'absD': 197605142784, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 168, 'ainvs': [0, 0, 0, -1911, -24010], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 7056, 'degree': 6144, 'elladic_images': ['8.48.0.138'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.87690893278185422559128831336', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 4], 'jinv': [35152, 9], 'lmfdb_iso': '7056.q', 'lmfdb_label': '7056.q4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -4, 4], 'min_quad_twist_disc': -84, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.h.1', '12.24.0.c.1', '24.96.1.bu.1', '28.24.0-4.b.1.2', '56.96.0-8.h.1.4', '84.48.0.?', '168.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.5811591095723577481912334398', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 441], [3, 8, 784], [7, 26, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1074504064531541456038320911', 'prec': 103}, 'szpiro_ratio': 3.8683329080987265, '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, -2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, -2, 0, 4, 2, 2, -4, -8, -6, 8, 6, -6, -4, 0, 2, -4, 2, 4, 8, -10, 8, 4, -6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 7056, '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': '7056.q', 'trace_hash': 2136425971010838049}
• 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': '0.17311176275863994669345206354', 'prec': 103}, 'conductor': 7056, 'gens': [[-26, 90, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.5811591095723577481912334398', 'prec': 100}], 'lmfdb_label': '7056.q4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.73572177178356058870019376674', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.7980299066997052931404217963894965804', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-14, 0, 1], [49, 0, 1]], 'xcoord_integral_points': [-35, -26, -14, 49, 161]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [3, 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': '7056.q4'}
• ec_torsion_growth •

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

  
  
  • id: 370926
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '7056.q4', 'torsion': [2, 4]}
  • id: 370927
    {'degree': 4, 'field': [1, 0, -5, 0, 1], 'lmfdb_label': '7056.q4', 'torsion': [2, 4]}
  • id: 370928
    {'degree': 4, 'field': [4, -2, -1, -1, 1], 'lmfdb_label': '7056.q4', 'torsion': [2, 4]}
  • id: 370930
    {'degree': 8, 'field': [-3, 30, -18, -18, -5, 14, 0, -4, 1], 'lmfdb_label': '7056.q4', 'torsion': [2, 8]}
  • id: 370929
    {'degree': 8, 'field': [16, 0, 12, 0, 5, 0, 3, 0, 1], 'lmfdb_label': '7056.q4', 'torsion': [4, 4]}
  • id: 370932
    {'degree': 8, 'field': [16, 0, 48, 0, 65, 0, 12, 0, 1], 'lmfdb_label': '7056.q4', 'torsion': [2, 8]}
  • id: 370933
    {'degree': 8, 'field': [347, -730, -404, -496, 260, 22, -10, -4, 1], 'lmfdb_label': '7056.q4', 'torsion': [2, 6]}
  • id: 370931
    {'degree': 8, 'field': [625, 0, 0, 0, 71, 0, 0, 0, 1], 'lmfdb_label': '7056.q4', 'torsion': [2, 8]}
  • id: 370935
    {'degree': 16, 'field': [256, -512, 512, -448, 368, -496, 648, -780, 481, -12, -24, 14, -1, 2, 2, -2, 1], 'lmfdb_label': '7056.q4', 'torsion': [4, 8]}
  • id: 370936
    {'degree': 16, 'field': [256, 0, 0, 0, -16, 0, 0, 0, -15, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '7056.q4', 'torsion': [4, 8]}
  • id: 370934
    {'degree': 16, 'field': [256, 0, 768, 0, 1072, 0, 648, 0, 81, 0, -108, 0, 19, 0, -6, 0, 1], 'lmfdb_label': '7056.q4', 'torsion': [2, 8]}
  • id: 370937
    {'degree': 16, 'field': [8836, -1504, -16192, -176440, 264516, 26048, 41628, 16700, -24176, 1036, 5448, 16, -228, 16, -10, -2, 1], 'lmfdb_label': '7056.q4', '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: 144633
    {'conductor': 7056, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '7056.q4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 144634
    {'conductor': 7056, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '7056.q4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 144635
    {'conductor': 7056, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '7056.q4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1710729
    {'adelic_gens': [[139, 112, 98, 69], [113, 0, 112, 29], [1, 0, 8, 1], [1, 8, 0, 1], [161, 8, 160, 9], [5, 4, 164, 165], [95, 0, 0, 167], [97, 70, 42, 125]], 'adelic_image': '168.192.1.?', 'conductor': 7056, 'lmfdb_label': '7056.q4', 'prime': 0}
  • id: 34919
    {'conductor': 7056, 'elladic_image': '8.48.0.138', 'lmfdb_label': '7056.q4', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 285596
    {'lmfdb_iso': '7056.q', 'p': 5, 'prec': 20, 'unit': 1692725606352, 'val': 1}
  • id: 285604
    {'lmfdb_iso': '7056.q', 'p': 11, 'prec': 20, 'unit': 20573822734769631590, 'val': 1}
  • id: 285602
    {'lmfdb_iso': '7056.q', 'p': 13, 'prec': 20, 'unit': 385162931278710485893, 'val': 1}
  • id: 285605
    {'lmfdb_iso': '7056.q', 'p': 17, 'prec': 20, 'unit': 2897341003212692728564, 'val': 2}
  • id: 285606
    {'lmfdb_iso': '7056.q', 'p': 19, 'prec': 20, 'unit': 868982495581365896191599, 'val': 1}
  • id: 285609
    {'lmfdb_iso': '7056.q', 'p': 23, 'prec': 20, 'unit': 20854862995411147886239167, 'val': 1}
  • id: 285601
    {'lmfdb_iso': '7056.q', 'p': 29, 'prec': 20, 'unit': 376126278920404766196007668, 'val': 1}
  • id: 285598
    {'lmfdb_iso': '7056.q', 'p': 31, 'prec': 20, 'unit': 16824721664049102849968115323, 'val': 1}
  • id: 285613
    {'lmfdb_iso': '7056.q', 'p': 37, 'prec': 20, 'unit': 217141843950839179187314541751, 'val': 1}
  • id: 285599
    {'lmfdb_iso': '7056.q', 'p': 41, 'prec': 20, 'unit': 879327902943622460119867845619, 'val': 1}
  • id: 285600
    {'lmfdb_iso': '7056.q', 'p': 43, 'prec': 20, 'unit': 3490549681464487350432857322798, 'val': 1}
  • id: 285607
    {'lmfdb_iso': '7056.q', 'p': 53, 'prec': 20, 'unit': 208789443719950295319583205724371, 'val': 1}
  • id: 285611
    {'lmfdb_iso': '7056.q', 'p': 59, 'prec': 20, 'unit': 284006398357855956196249242385801, 'val': 1}
  • id: 285612
    {'lmfdb_iso': '7056.q', 'p': 61, 'prec': 20, 'unit': 8017269362870967771961770890087076, 'val': 1}
  • id: 285595
    {'lmfdb_iso': '7056.q', 'p': 67, 'prec': 20, 'unit': 16771748017825594257321376808440818, 'val': 1}
  • id: 285597
    {'lmfdb_iso': '7056.q', 'p': 71, 'prec': 20, 'unit': 53076997929551413603592354391943997, 'val': 1}
  • id: 285608
    {'lmfdb_iso': '7056.q', 'p': 73, 'prec': 20, 'unit': 60830877517718459035846899924724060, 'val': 1}
  • id: 285603
    {'lmfdb_iso': '7056.q', 'p': 79, 'prec': 20, 'unit': 10679375910988284597786921798726816, 'val': 1}
  • id: 285594
    {'lmfdb_iso': '7056.q', 'p': 83, 'prec': 20, 'unit': 1117676197826661714503252444342723298, 'val': 1}
  • id: 285610
    {'lmfdb_iso': '7056.q', 'p': 89, 'prec': 20, 'unit': 4047194903387916509450889757178314058, 'val': 1}
  • id: 285593
    {'lmfdb_iso': '7056.q', 'p': 97, 'prec': 20, 'unit': 3781807592752538122286554687236205929, 'val': 1}