Elliptic curve data - 47040.s2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '47040dz', 'Clabel': '47040dz1', 'Cnumber': 1, 'abc_quality': 1.2666941259754438, 'absD': 2116800, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 168, 'ainvs': [0, -1, 0, 19, -69], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 47040, 'degree': 6912, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.10281621354538887354700423372', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 3], 'jinv': [229376, 675], 'lmfdb_iso': '47040.s', 'lmfdb_label': '47040.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, 5, 6], 'min_quad_twist_disc': -8, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0.b.1', '168.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3762100776403974139730967995', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 147], [3, 4, 15680], [5, 6, 9408], [7, 14, 960]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.77370816200124707910651241836', 'prec': 107}, 'szpiro_ratio': 2.026365543991817, '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, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, -6, 0, -5, 0], 'aplist': [0, -1, -1, 0, 0, -1, -6, -5, -6, 6, 5, 7, -12, -1, 6, 0, 6, 2, -7, -12, -11, 13, 12, -6, 10], 'class_deg': 3, 'class_size': 2, 'conductor': 47040, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '47040.s', 'trace_hash': 1829966676938231889}
• 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': '1.2283016306035602845283387984', 'prec': 100}, 'conductor': 47040, 'gens': [[6, 15, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3762100776403974139730967995', 'prec': 100}], 'lmfdb_label': '47040.s2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.3375146055657327074243873268', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6814021583415650648029527280215882466', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [6]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': 'a', '11': [1, 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, 0]}, 'iwp0': 0, 'lmfdb_label': '47040.s2'}
• ec_torsion_growth •

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

  
  
  • id: 2294897
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '47040.s2', 'torsion': [3]}
  • id: 2294898
    {'degree': 3, 'field': [1, 5, -1, 1], 'lmfdb_label': '47040.s2', 'torsion': [2]}
  • id: 2294901
    {'degree': 6, 'field': [-126, 0, 84, 0, -14, 0, 1], 'lmfdb_label': '47040.s2', 'torsion': [6]}
  • id: 2294899
    {'degree': 6, 'field': [27, 9, -8, -3, 4, -3, 1], 'lmfdb_label': '47040.s2', 'torsion': [2, 2]}
  • id: 2294900
    {'degree': 6, 'field': [672, 0, 532, 0, 14, 0, 1], 'lmfdb_label': '47040.s2', 'torsion': [3]}
  • id: 2294902
    {'degree': 12, 'field': [-90, -192, -7368, 2228, 5296, -892, -2234, 1116, -150, -16, 10, -4, 1], 'lmfdb_label': '47040.s2', 'torsion': [4]}
  • id: 2294904
    {'degree': 12, 'field': [15876, 0, 10584, 0, 5292, 0, 924, 0, 112, 0, 14, 0, 1], 'lmfdb_label': '47040.s2', 'torsion': [2, 6]}
  • id: 2294903
    {'degree': 12, 'field': [451584, 0, -357504, 0, 273616, 0, -6104, 0, -336, 0, -14, 0, 1], 'lmfdb_label': '47040.s2', 'torsion': [3, 3]}
  • id: 2294906
    {'degree': 18, 'field': [74088, 0, 0, 0, 0, 0, 13132, 0, 0, 0, 0, 0, 686, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '47040.s2', 'torsion': [6]}
  • id: 2294905
    {'degree': 18, 'field': [735025537, 627723336, -365877576, -291356786, 102509751, 48418458, -14812165, -3468672, -105906, 1786, 208464, 16452, -5968, 492, -906, -92, 9, -6, 1], 'lmfdb_label': '47040.s2', 'torsion': [9]}
• 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: 1122786
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '47040.s2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1122787
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '47040.s2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1122788
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '47040.s2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1122789
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '47040.s2', 'prime': 7, 'reduction_type': 0, '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: 1977771
    {'adelic_gens': [[4, 3, 9, 7], [163, 6, 162, 7], [37, 6, 36, 7], [1, 6, 0, 1], [83, 0, 0, 167], [1, 0, 6, 1], [43, 0, 0, 1], [3, 4, 8, 11], [159, 166, 152, 161], [132, 155, 137, 156]], 'adelic_image': '168.16.0.?', 'conductor': 47040, 'lmfdb_label': '47040.s2', 'prime': 0}
  • id: 203697
    {'conductor': 47040, 'elladic_image': '3.4.0.1', 'lmfdb_label': '47040.s2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2358931
    {'lmfdb_iso': '47040.s', 'p': 13, 'prec': 20, 'unit': 1369565936644640310696, 'val': 1}
  • id: 2358933
    {'lmfdb_iso': '47040.s', 'p': 17, 'prec': 20, 'unit': 28834780456094490259042, 'val': 1}
  • id: 2358934
    {'lmfdb_iso': '47040.s', 'p': 19, 'prec': 20, 'unit': 1595771704836696244918215, 'val': 1}
  • id: 2358937
    {'lmfdb_iso': '47040.s', 'p': 23, 'prec': 20, 'unit': 49956851752569825429185631, 'val': 1}
  • id: 2358930
    {'lmfdb_iso': '47040.s', 'p': 29, 'prec': 20, 'unit': 5213149766961603395788872300, 'val': 1}
  • id: 2358941
    {'lmfdb_iso': '47040.s', 'p': 31, 'prec': 20, 'unit': 13812999645245458924451853544, 'val': 1}
  • id: 2358926
    {'lmfdb_iso': '47040.s', 'p': 37, 'prec': 20, 'unit': 148404292524574086444245151856, 'val': 1}
  • id: 2358928
    {'lmfdb_iso': '47040.s', 'p': 41, 'prec': 20, 'unit': 4304664641078465284251614085418, 'val': 1}
  • id: 2358929
    {'lmfdb_iso': '47040.s', 'p': 43, 'prec': 20, 'unit': 5200842804241148366593359906879, 'val': 1}
  • id: 2358939
    {'lmfdb_iso': '47040.s', 'p': 47, 'prec': 20, 'unit': 46027248411029765002703205387766, 'val': 1}
  • id: 2358935
    {'lmfdb_iso': '47040.s', 'p': 59, 'prec': 20, 'unit': 4312635696263392554057243726543426, 'val': 1}
  • id: 2358940
    {'lmfdb_iso': '47040.s', 'p': 61, 'prec': 20, 'unit': 2349166722999601191353046890206986, 'val': 1}
  • id: 2358925
    {'lmfdb_iso': '47040.s', 'p': 67, 'prec': 20, 'unit': 28200735988926657768500572158906610, 'val': 1}
  • id: 2358927
    {'lmfdb_iso': '47040.s', 'p': 71, 'prec': 20, 'unit': 131506563978475987162000730594531253, 'val': 1}
  • id: 2358936
    {'lmfdb_iso': '47040.s', 'p': 73, 'prec': 20, 'unit': 221759306622711867848102138553568267, 'val': 1}
  • id: 2358932
    {'lmfdb_iso': '47040.s', 'p': 79, 'prec': 20, 'unit': 235408166511846541909392492363220065, 'val': 1}
  • id: 2358924
    {'lmfdb_iso': '47040.s', 'p': 83, 'prec': 20, 'unit': 1374178853979571480052207840853375383, 'val': 1}
  • id: 2358938
    {'lmfdb_iso': '47040.s', 'p': 89, 'prec': 20, 'unit': 5986091149457180566648380513802129968, 'val': 1}
  • id: 2358923
    {'lmfdb_iso': '47040.s', 'p': 97, 'prec': 20, 'unit': 35483538635840735447606979732053352178, 'val': 1}