Elliptic curve data - 64320.cs1

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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': '64320ct', 'Clabel': '64320ct2', 'Cnumber': 2, 'abc_quality': 0.9560396492729272, 'absD': 14071069305077760, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 8040, 'ainvs': [0, 1, 0, -196225, 32900735], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 67], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 64320, 'degree': 487424, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8965985106421555736534451976', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 70, 'isogeny_degrees': [1, 2], 'jinv': [6374982726455618, 107353739205], 'lmfdb_iso': '64320.cs', 'lmfdb_label': '64320.cs1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -49056, -4137120], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '40.6.0.b.1', '804.6.0.?', '8040.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5727175003083083913239649719', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 5], [3, 4, 21440], [5, 6, 12864], [7, 2, 21440], [67, 68, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.91464000484889971864569969220', 'prec': 103}, 'szpiro_ratio': 4.351182045369736, '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, 2, 0, 1, 0, 0, 0, -6, 0, 1, 0, 0, 0, 0, 0], 'aplist': [0, 1, 1, 2, 0, -6, 0, 0, 2, -4, -8, 6, -6, 8, 6, 2, 2, -4, 1, 8, 2, 0, 16, -10, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 64320, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '64320.cs', 'trace_hash': 1963787000170131650}
• 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': '0.022523478582315395367343214947', 'prec': 107}, 'conductor': 64320, 'gens': [[218, 729, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5727175003083083913239649719', 'prec': 100}], 'lmfdb_label': '64320.cs1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.39677208467595021477711220342', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.7361456168514765308038966061234061891', 'prec': 130}, 'tamagawa_product': 56, 'torsion_generators': [[-511, 0, 1]], 'xcoord_integral_points': [-511, 218, 293]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': [1, 0], '11': [1, 1, 0], '13': [3, 0], '17': [1, 1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '67': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '64320.cs1'}
• ec_torsion_growth •

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

  
  
  • id: 3073644
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '64320.cs1', 'torsion': [2, 2]}
  • id: 3073645
    {'degree': 4, 'field': [40, 0, 19, 0, 1], 'lmfdb_label': '64320.cs1', 'torsion': [4]}
  • id: 3073648
    {'degree': 8, 'field': [-115248, 0, -12352, 0, -1176, 0, 0, 0, 1], 'lmfdb_label': '64320.cs1', 'torsion': [6]}
  • id: 3073646
    {'degree': 8, 'field': [12321, 0, -23636, 0, 2306, 0, -76, 0, 1], 'lmfdb_label': '64320.cs1', 'torsion': [2, 4]}
  • id: 3073647
    {'degree': 8, 'field': [108900, 0, -8700, 0, 661, 0, -2, 0, 1], 'lmfdb_label': '64320.cs1', 'torsion': [2, 4]}
  • id: 3073650
    {'degree': 16, 'field': [1830609, 0, -158292, 0, 30060, 0, -124684, 0, 10310, 0, -1996, 0, 28, 0, -20, 0, 1], 'lmfdb_label': '64320.cs1', 'torsion': [2, 6]}
  • id: 3073649
    {'degree': 16, 'field': [10656307360000, 0, 75372424000, 0, 7195368100, 0, -624255260, 0, 29292961, 0, -737348, 0, 13054, 0, -128, 0, 1], 'lmfdb_label': '64320.cs1', 'torsion': [8]}
• 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: 1553105
    {'conductor': 64320, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '64320.cs1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1553106
    {'conductor': 64320, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '64320.cs1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 14}
  • id: 1553107
    {'conductor': 64320, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '64320.cs1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1553108
    {'conductor': 64320, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '64320.cs1', 'prime': 67, '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: 2090108
    {'adelic_gens': [[6434, 1, 4823, 0], [5161, 4, 2282, 9], [2681, 4, 5362, 9], [1, 2, 2, 5], [1, 0, 4, 1], [2, 1, 4019, 0], [1, 4, 0, 1], [3017, 5026, 5024, 3015], [3, 4, 8, 11], [8037, 4, 8036, 5]], 'adelic_image': '8040.12.0.?', 'conductor': 64320, 'lmfdb_label': '64320.cs1', 'prime': 0}
  • id: 269924
    {'conductor': 64320, 'elladic_image': '2.3.0.1', 'lmfdb_label': '64320.cs1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3278572
    {'lmfdb_iso': '64320.cs', 'p': 7, 'prec': 20, 'unit': 62283787036869757, 'val': 0}
  • id: 3278576
    {'lmfdb_iso': '64320.cs', 'p': 13, 'prec': 20, 'unit': 64188408987728608468, 'val': 2}
  • id: 3278581
    {'lmfdb_iso': '64320.cs', 'p': 23, 'prec': 20, 'unit': 15155060133067723343260335, 'val': 1}
  • id: 3278575
    {'lmfdb_iso': '64320.cs', 'p': 29, 'prec': 20, 'unit': 4820011793446874475773820960, 'val': 1}
  • id: 3278586
    {'lmfdb_iso': '64320.cs', 'p': 31, 'prec': 20, 'unit': 93685747075983669104358711, 'val': 1}
  • id: 3278571
    {'lmfdb_iso': '64320.cs', 'p': 37, 'prec': 20, 'unit': 186502670540779862344408403058, 'val': 1}
  • id: 3278573
    {'lmfdb_iso': '64320.cs', 'p': 41, 'prec': 20, 'unit': 3337947371323727134579987370932, 'val': 1}
  • id: 3278574
    {'lmfdb_iso': '64320.cs', 'p': 43, 'prec': 20, 'unit': 9186809067528246707014947043971, 'val': 1}
  • id: 3278577
    {'lmfdb_iso': '64320.cs', 'p': 47, 'prec': 20, 'unit': 14268240486115712050587301001879, 'val': 1}
  • id: 3278579
    {'lmfdb_iso': '64320.cs', 'p': 53, 'prec': 20, 'unit': 300767354853224260799699773925395, 'val': 1}
  • id: 3278584
    {'lmfdb_iso': '64320.cs', 'p': 59, 'prec': 20, 'unit': 2628690331834709130666025425651796, 'val': 1}
  • id: 3278585
    {'lmfdb_iso': '64320.cs', 'p': 61, 'prec': 20, 'unit': 1517447164218749711228603987468601, 'val': 1}
  • id: 3278583
    {'lmfdb_iso': '64320.cs', 'p': 71, 'prec': 20, 'unit': 32978694011226140264115045790040899, 'val': 1}
  • id: 3278580
    {'lmfdb_iso': '64320.cs', 'p': 73, 'prec': 20, 'unit': 55156880661318789553558650970760484, 'val': 1}
  • id: 3278578
    {'lmfdb_iso': '64320.cs', 'p': 83, 'prec': 20, 'unit': 696616544762953095910945235553067986, 'val': 1}
  • id: 3278582
    {'lmfdb_iso': '64320.cs', 'p': 89, 'prec': 20, 'unit': 5807872681725792520570200674205460488, 'val': 1}
  • id: 3278570
    {'lmfdb_iso': '64320.cs', 'p': 97, 'prec': 20, 'unit': 35696106409015201018206483828701812328, 'val': 1}