Elliptic curve data - 2420.a4

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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': '2420e', 'Clabel': '2420e2', 'Cnumber': 2, 'abc_quality': 0.8396384887826309, 'absD': 11337990400, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 1320, 'ainvs': [0, 1, 0, 444, -3500], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 2420, 'degree': 1440, 'elladic_images': ['4.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.61557113116363795556556176914', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [21296, 25], 'lmfdb_iso': '2420.a', 'lmfdb_label': '2420.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 4, 4], 'min_quad_twist_disc': -11, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.a.1', '6.12.0.a.1', '12.24.0.d.1', '20.12.0.d.1', '24.48.0.bh.1', '33.8.0-3.a.1.2', '40.24.0.bc.1', '60.48.1.h.1', '66.24.0-6.a.1.2', '88.12.0.?', '120.192.9.?', '132.48.0.?', '264.96.0.?', '440.48.0.?', '660.96.1.?', '1320.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.9130372864494544052749328194', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 121], [5, 6, 484], [11, 62, 20]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0454746256088441894102314341', 'prec': 103}, 'szpiro_ratio': 3.840965921994184, '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, -2, 0, -1, 0, -2, 0, 1, 0, 0, 0, -2, 0, 2, 0, 6, 0, 4, 0], 'aplist': [0, -2, -1, -2, 0, -2, 6, 4, 6, -6, -4, 2, -6, 10, -6, -6, 12, -2, 2, -12, -2, -8, -6, -6, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 2420, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '2420.a', 'trace_hash': 1658854848688356346}
• 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': '0.29195889349455137159852019069', 'prec': 103}, 'conductor': 2420, 'gens': [[27, 170, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9130372864494544052749328194', 'prec': 100}], 'lmfdb_label': '2420.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.68568660695483384601994767611', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9974306528784427775247617405225978780', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[7, 0, 1]], 'xcoord_integral_points': [7, 27]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': [3, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '2420.a4'}
• ec_torsion_growth •

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

  
  
  • id: 124234
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [2, 2]}
  • id: 124235
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '2420.a4', 'torsion': [6]}
  • id: 124236
    {'degree': 4, 'field': [-121, 0, -11, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [4]}
  • id: 124237
    {'degree': 4, 'field': [9, 0, -5, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [2, 6]}
  • id: 124238
    {'degree': 6, 'field': [66, -198, 136, -27, 1, -3, 1], 'lmfdb_label': '2420.a4', 'torsion': [6]}
  • id: 124241
    {'degree': 8, 'field': [81, 0, 45, 0, 2, 0, -5, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [12]}
  • id: 124240
    {'degree': 8, 'field': [361, 608, 512, -198, 63, 22, 2, -2, 1], 'lmfdb_label': '2420.a4', 'torsion': [2, 4]}
  • id: 124239
    {'degree': 8, 'field': [676, 0, -536, 0, 196, 0, -24, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [2, 4]}
  • id: 124242
    {'degree': 12, 'field': [36, 0, 2292, 0, 1036, 0, 503, 0, 111, 0, 17, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [3, 6]}
  • id: 124243
    {'degree': 12, 'field': [576, 0, 2352, 0, 1276, 0, 973, 0, 291, 0, 7, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [2, 6]}
  • id: 124246
    {'degree': 16, 'field': [1049, -4148, 7666, -9780, 4558, 8784, -9878, -2576, 5591, 212, -1690, 48, 308, -4, -28, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [2, 12]}
  • id: 124244
    {'degree': 16, 'field': [3721, 0, 312456, 0, 474346, 0, 300716, 0, 94999, 0, 15724, 0, 1378, 0, 60, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [4, 4]}
  • id: 124247
    {'degree': 16, 'field': [6561, -4374, 1458, -6804, 6642, 54, 2016, -1806, 43, -602, 224, 2, 82, -28, 2, -2, 1], 'lmfdb_label': '2420.a4', 'torsion': [2, 12]}
  • id: 124245
    {'degree': 16, 'field': [25361296, 0, -442848, 0, -2057200, 0, 557232, 0, -34916, 0, -5352, 0, 940, 0, -52, 0, 1], 'lmfdb_label': '2420.a4', 'torsion': [8]}
  • id: 124248
    {'degree': 18, 'field': [18847, -59406, 85737, -76973, 114273, -68361, 79105, -41055, 34023, -15032, 10158, -3567, 2171, -591, 309, -62, 27, -3, 1], 'lmfdb_label': '2420.a4', 'torsion': [18]}
• 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: 41396
    {'conductor': 2420, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '2420.a4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 41397
    {'conductor': 2420, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2420.a4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 41398
    {'conductor': 2420, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '2420.a4', 'prime': 11, '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: 1679698
    {'adelic_gens': [[1297, 24, 1296, 25], [1299, 616, 286, 243], [13, 24, 612, 13], [661, 264, 726, 265], [1, 24, 0, 1], [111, 484, 143, 1013], [15, 16, 314, 335], [119, 0, 0, 1319], [1, 0, 24, 1], [837, 1210, 44, 221]], 'adelic_image': '1320.384.9.?', 'conductor': 2420, 'lmfdb_label': '2420.a4', 'prime': 0}
  • id: 11960
    {'conductor': 2420, 'elladic_image': '4.6.0.5', 'lmfdb_label': '2420.a4', 'modell_image': '2B', 'prime': 2}
  • id: 11961
    {'conductor': 2420, 'elladic_image': '3.4.0.1', 'lmfdb_label': '2420.a4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 74317
    {'lmfdb_iso': '2420.a', 'p': 7, 'prec': 20, 'unit': 392832166814923, 'val': 2}
  • id: 74321
    {'lmfdb_iso': '2420.a', 'p': 13, 'prec': 20, 'unit': 660761142145630139084, 'val': 1}
  • id: 74323
    {'lmfdb_iso': '2420.a', 'p': 17, 'prec': 20, 'unit': 160160182269902818639354, 'val': 1}
  • id: 74324
    {'lmfdb_iso': '2420.a', 'p': 19, 'prec': 20, 'unit': 790559765781974319136312, 'val': 1}
  • id: 74328
    {'lmfdb_iso': '2420.a', 'p': 23, 'prec': 20, 'unit': 29960170915722009794260729, 'val': 1}
  • id: 74320
    {'lmfdb_iso': '2420.a', 'p': 29, 'prec': 20, 'unit': 4361602790230168112515823649, 'val': 1}
  • id: 74333
    {'lmfdb_iso': '2420.a', 'p': 31, 'prec': 20, 'unit': 91589927617864928893292531, 'val': 2}
  • id: 74316
    {'lmfdb_iso': '2420.a', 'p': 37, 'prec': 20, 'unit': 71062844115467142327959893980, 'val': 1}
  • id: 74318
    {'lmfdb_iso': '2420.a', 'p': 41, 'prec': 20, 'unit': 4171113241907642148058693655726, 'val': 1}
  • id: 74319
    {'lmfdb_iso': '2420.a', 'p': 43, 'prec': 20, 'unit': 6886261692886010928218403336116, 'val': 1}
  • id: 74331
    {'lmfdb_iso': '2420.a', 'p': 47, 'prec': 20, 'unit': 42013766609015320851627364851646, 'val': 1}
  • id: 74325
    {'lmfdb_iso': '2420.a', 'p': 53, 'prec': 20, 'unit': 443609281216645212462456775496801, 'val': 1}
  • id: 74326
    {'lmfdb_iso': '2420.a', 'p': 59, 'prec': 20, 'unit': 659989046235739803917380697562488, 'val': 1}
  • id: 74332
    {'lmfdb_iso': '2420.a', 'p': 61, 'prec': 20, 'unit': 4594844118151921754817743770530789, 'val': 1}
  • id: 74315
    {'lmfdb_iso': '2420.a', 'p': 67, 'prec': 20, 'unit': 21389338965187411381594710789558335, 'val': 1}
  • id: 74330
    {'lmfdb_iso': '2420.a', 'p': 71, 'prec': 20, 'unit': 12847490589873206090654263227101591, 'val': 1}
  • id: 74327
    {'lmfdb_iso': '2420.a', 'p': 73, 'prec': 20, 'unit': 90095723965563517922442124970329873, 'val': 1}
  • id: 74322
    {'lmfdb_iso': '2420.a', 'p': 79, 'prec': 20, 'unit': 436766174967177885429381560490094711, 'val': 1}
  • id: 74314
    {'lmfdb_iso': '2420.a', 'p': 83, 'prec': 20, 'unit': 2524599695279598883064091342629927334, 'val': 1}
  • id: 74329
    {'lmfdb_iso': '2420.a', 'p': 89, 'prec': 20, 'unit': 1684179471486913956314446349952026228, 'val': 1}
  • id: 74313
    {'lmfdb_iso': '2420.a', 'p': 97, 'prec': 20, 'unit': 15716499391802050511588867547225711627, 'val': 1}