Elliptic curve data - 7056.w1

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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': '7056bk', 'Clabel': '7056bk2', 'Cnumber': 2, 'abc_quality': 1.032335220248665, 'absD': 4818707323144372224, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 168, 'ainvs': [0, 0, 0, -995043, -396371486], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 7056, 'degree': 112896, 'elladic_images': ['7.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3498849629083107785302448179', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 7, 'iso_nlabel': 22, 'isogeny_degrees': [1, 7], 'jinv': [-6329617441, 279936], 'lmfdb_iso': '7056.w', 'lmfdb_label': '7056.w1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -141, 657], 'min_quad_twist_disc': -84, 'modell_images': ['7B.6.1'], 'modm_images': ['7.24.0.a.1', '24.2.0.b.1', '56.48.0-7.a.1.8', '84.48.0.?', '168.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2542231648526864448987732701', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 441], [3, 8, 784], [7, 26, 144]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.18984179468923157998817841765', 'prec': 107}, 'szpiro_ratio': 5.994252617526152, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 4, 0, -8, 0], 'aplist': [0, 0, -1, 0, 5, 0, 4, -8, -4, 5, -3, -4, 0, -2, -6, 9, -11, -6, 2, 2, 10, -3, -7, 6, 7], 'class_deg': 7, 'class_size': 2, 'conductor': 7056, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '7056.w', 'trace_hash': 1198351147755889894}
• 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': '0.0090973699308913426230125789161', 'prec': 110}, 'conductor': 7056, 'gens': [[4655, 309582, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2542231648526864448987732701', 'prec': 100}], 'lmfdb_label': '7056.w1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.075385467085302682385699667347', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0784559887262968762683008998209008924', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': [4655]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': 'a', '11': [1, 0], '13': [1, 1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '7056.w1'}
• ec_torsion_growth •

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

  
  
  • id: 371249
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '7056.w1', 'torsion': [7]}
  • id: 371250
    {'degree': 3, 'field': [-6, -2, -1, 1], 'lmfdb_label': '7056.w1', 'torsion': [2]}
  • id: 371251
    {'degree': 6, 'field': [6, 0, 13, 0, 16, 0, 1], 'lmfdb_label': '7056.w1', 'torsion': [2, 2]}
  • id: 371252
    {'degree': 6, 'field': [84, 0, 49, 0, 14, 0, 1], 'lmfdb_label': '7056.w1', 'torsion': [14]}
  • id: 371253
    {'degree': 8, 'field': [-48, 0, -60, 0, -36, 0, -4, 0, 1], 'lmfdb_label': '7056.w1', 'torsion': [3]}
  • id: 371255
    {'degree': 12, 'field': [36, 0, -24, 0, 436, 0, 148, 0, 81, 0, 16, 0, 1], 'lmfdb_label': '7056.w1', 'torsion': [2, 14]}
  • id: 371254
    {'degree': 12, 'field': [36, 60, 144, -68, -264, -116, 112, 156, 53, -9, -12, -1, 1], 'lmfdb_label': '7056.w1', 'torsion': [4]}
  • id: 371256
    {'degree': 16, 'field': [7056, 0, 7056, 0, 1764, 0, 8421, 0, -210, 0, 105, 0, 25, 0, 10, 0, 1], 'lmfdb_label': '7056.w1', 'torsion': [21]}
• 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: 144717
    {'conductor': 7056, 'conductor_valuation': 4, 'discriminant_valuation': 19, 'j_denominator_valuation': 7, 'kodaira_symbol': -15, 'lmfdb_label': '7056.w1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 144718
    {'conductor': 7056, 'conductor_valuation': 2, 'discriminant_valuation': 13, 'j_denominator_valuation': 7, 'kodaira_symbol': -11, 'lmfdb_label': '7056.w1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 144719
    {'conductor': 7056, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '7056.w1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1710737
    {'adelic_gens': [[1, 0, 14, 1], [104, 161, 119, 6], [8, 7, 77, 162], [8, 5, 91, 57], [155, 14, 154, 15], [125, 70, 0, 53], [41, 154, 0, 167], [1, 14, 0, 1]], 'adelic_image': '168.96.2.?', 'conductor': 7056, 'lmfdb_label': '7056.w1', 'prime': 0}
  • id: 34924
    {'conductor': 7056, 'elladic_image': '7.24.0.1', 'lmfdb_label': '7056.w1', 'modell_image': '7B.6.1', 'prime': 7}
• ec_padic •

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

  
  
  • id: 285657
    {'lmfdb_iso': '7056.w', 'p': 5, 'prec': 20, 'unit': 3410726200211, 'val': 2}
  • id: 285664
    {'lmfdb_iso': '7056.w', 'p': 11, 'prec': 20, 'unit': 40855371466422201103, 'val': 1}
  • id: 285665
    {'lmfdb_iso': '7056.w', 'p': 17, 'prec': 20, 'unit': 144095469780926125469084, 'val': 1}
  • id: 285666
    {'lmfdb_iso': '7056.w', 'p': 19, 'prec': 20, 'unit': 1562746121986471074827351, 'val': 1}
  • id: 285669
    {'lmfdb_iso': '7056.w', 'p': 23, 'prec': 20, 'unit': 38114070176722490460770984, 'val': 1}
  • id: 285662
    {'lmfdb_iso': '7056.w', 'p': 29, 'prec': 20, 'unit': 3958469545679206458655145191, 'val': 1}
  • id: 285659
    {'lmfdb_iso': '7056.w', 'p': 31, 'prec': 20, 'unit': 4042500396851786935636784876, 'val': 1}
  • id: 285673
    {'lmfdb_iso': '7056.w', 'p': 37, 'prec': 20, 'unit': 136572917699955506199224104455, 'val': 1}
  • id: 285661
    {'lmfdb_iso': '7056.w', 'p': 43, 'prec': 20, 'unit': 255887736220066088372544714346, 'val': 1}
  • id: 285671
    {'lmfdb_iso': '7056.w', 'p': 47, 'prec': 20, 'unit': 51779039408062903052007393472946, 'val': 1}
  • id: 285667
    {'lmfdb_iso': '7056.w', 'p': 53, 'prec': 20, 'unit': 67721673170255592894659747770621, 'val': 1}
  • id: 285668
    {'lmfdb_iso': '7056.w', 'p': 59, 'prec': 20, 'unit': 4342064950440534382495731803278265, 'val': 1}
  • id: 285672
    {'lmfdb_iso': '7056.w', 'p': 61, 'prec': 20, 'unit': 7544563716263415524692780652119058, 'val': 1}
  • id: 285656
    {'lmfdb_iso': '7056.w', 'p': 67, 'prec': 20, 'unit': 37916801390804182265486126611333774, 'val': 1}
  • id: 285658
    {'lmfdb_iso': '7056.w', 'p': 71, 'prec': 20, 'unit': 140589796562553257787031776139366312, 'val': 1}
  • id: 285660
    {'lmfdb_iso': '7056.w', 'p': 73, 'prec': 20, 'unit': 94683460952377823531752093270825693, 'val': 1}
  • id: 285663
    {'lmfdb_iso': '7056.w', 'p': 79, 'prec': 20, 'unit': 521106050114460163455011159077708361, 'val': 1}
  • id: 285655
    {'lmfdb_iso': '7056.w', 'p': 83, 'prec': 20, 'unit': 352327862309547040962698461752692880, 'val': 1}
  • id: 285670
    {'lmfdb_iso': '7056.w', 'p': 89, 'prec': 20, 'unit': 8954450469754740428463122113194304082, 'val': 1}
  • id: 285654
    {'lmfdb_iso': '7056.w', 'p': 97, 'prec': 20, 'unit': 44139203209320075091784348086011005669, 'val': 1}