Elliptic curve data - 1584.k4

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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': '1584j', 'Clabel': '1584j1', 'Cnumber': 1, 'abc_quality': 0.9924779712445644, 'absD': 4982833152, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 132, 'ainvs': [0, 0, 0, -1035, -12358], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 1584, 'degree': 768, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.62663262616826026994514910742', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [1108717875, 45056], 'lmfdb_iso': '1584.k', 'lmfdb_label': '1584.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -582, -5068], 'min_quad_twist_disc': 12, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.48.0-12.i.1.4', '44.6.0.e.1', '66.24.0.b.1', '132.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6260403457123832600166257793', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 33], [3, 6, 176], [11, 12, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.34116762655871246232089432327', 'prec': 107}, 'szpiro_ratio': 4.403007099311436, '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, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 2, 0, 0, 0, -6, 0, -2, 0], 'aplist': [0, 0, 0, -2, 1, 2, -6, -2, 0, -6, 4, 2, 6, 10, -12, -12, -12, -10, -8, -12, 14, -2, 12, 0, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 1584, 'isogeny_matrix': [[1, 3, 2, 6], [3, 1, 6, 2], [2, 6, 1, 3], [6, 2, 3, 1]], 'lmfdb_iso': '1584.k', 'trace_hash': 1122240759570364325}
• 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': '0.28557081208064529418195365553', 'prec': 103}, 'conductor': 1584, 'gens': [[-17, 18, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6260403457123832600166257793', 'prec': 100}], 'lmfdb_label': '1584.k4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.84382374251097024059422519737', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7441828999857102497399234759446950426', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[37, 0, 1]], 'xcoord_integral_points': [-17, 37]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 3, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1584.k4'}
• ec_torsion_growth •

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

  
  
  • id: 78487
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '1584.k4', 'torsion': [2, 2]}
  • id: 78488
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1584.k4', 'torsion': [6]}
  • id: 78489
    {'degree': 4, 'field': [1, 4, -3, -2, 1], 'lmfdb_label': '1584.k4', 'torsion': [4]}
  • id: 78490
    {'degree': 4, 'field': [64, 0, 17, 0, 1], 'lmfdb_label': '1584.k4', 'torsion': [2, 6]}
  • id: 78491
    {'degree': 6, 'field': [94, -198, 27, -22, -9, 0, 1], 'lmfdb_label': '1584.k4', 'torsion': [6]}
  • id: 78493
    {'degree': 8, 'field': [1, 0, -11, 0, 24, 0, -11, 0, 1], 'lmfdb_label': '1584.k4', 'torsion': [2, 4]}
  • id: 78494
    {'degree': 8, 'field': [16, -32, 20, 4, -11, 2, 5, -4, 1], 'lmfdb_label': '1584.k4', 'torsion': [12]}
  • id: 78492
    {'degree': 8, 'field': [36, 0, 63, 0, 30, 0, 6, 0, 1], 'lmfdb_label': '1584.k4', 'torsion': [2, 4]}
  • id: 78497
    {'degree': 12, 'field': [-579, 522, 2133, -4380, -1725, 192, 942, 300, -105, -90, -27, 0, 1], 'lmfdb_label': '1584.k4', 'torsion': [12]}
  • id: 78496
    {'degree': 12, 'field': [4096, 0, -6144, 0, 3840, 0, -1291, 0, 240, 0, -24, 0, 1], 'lmfdb_label': '1584.k4', 'torsion': [2, 6]}
  • id: 78495
    {'degree': 12, 'field': [20736, 0, 9072, 0, 3537, 0, 477, 0, 72, 0, -3, 0, 1], 'lmfdb_label': '1584.k4', 'torsion': [3, 6]}
  • id: 78498
    {'degree': 16, 'field': [-11, 88, -242, 154, 494, -962, 262, 692, -461, -306, 394, -36, -110, 46, 4, -6, 1], 'lmfdb_label': '1584.k4', 'torsion': [8]}
  • id: 78500
    {'degree': 16, 'field': [256, 0, -64, 0, 16, 0, 32, 0, -20, 0, 8, 0, 1, 0, -1, 0, 1], 'lmfdb_label': '1584.k4', 'torsion': [2, 12]}
  • id: 78499
    {'degree': 16, 'field': [4096, -1024, 128, 256, -832, -128, 66, -222, 193, -18, 0, 34, -13, -8, 8, -4, 1], 'lmfdb_label': '1584.k4', 'torsion': [2, 12]}
  • id: 78501
    {'degree': 18, 'field': [4096, 0, 12288, 0, -6720, 0, 15684, 0, 110292, 0, 43080, 0, 7185, 0, 687, 0, 39, 0, 1], 'lmfdb_label': '1584.k4', '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: 24496
    {'conductor': 1584, 'conductor_valuation': 4, 'discriminant_valuation': 24, 'j_denominator_valuation': 12, 'kodaira_symbol': -20, 'lmfdb_label': '1584.k4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 24497
    {'conductor': 1584, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1584.k4', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 24498
    {'conductor': 1584, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1584.k4', 'prime': 11, 'reduction_type': 1, '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: 1674355
    {'adelic_gens': [[1, 12, 0, 1], [121, 12, 120, 13], [1, 6, 6, 37], [130, 3, 45, 124], [1, 0, 12, 1], [56, 11, 9, 100], [117, 74, 34, 127], [11, 2, 82, 123]], 'adelic_image': '132.96.1.?', 'conductor': 1584, 'lmfdb_label': '1584.k4', 'prime': 0}
  • id: 7588
    {'conductor': 1584, 'elladic_image': '2.3.0.1', 'lmfdb_label': '1584.k4', 'modell_image': '2B', 'prime': 2}
  • id: 7589
    {'conductor': 1584, 'elladic_image': '3.4.0.1', 'lmfdb_label': '1584.k4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 42216
    {'lmfdb_iso': '1584.k', 'p': 7, 'prec': 20, 'unit': 4739164654653785, 'val': 1}
  • id: 42220
    {'lmfdb_iso': '1584.k', 'p': 13, 'prec': 20, 'unit': 136563011234107368535, 'val': 1}
  • id: 42222
    {'lmfdb_iso': '1584.k', 'p': 17, 'prec': 20, 'unit': 85500668603570559055673, 'val': 1}
  • id: 42223
    {'lmfdb_iso': '1584.k', 'p': 19, 'prec': 20, 'unit': 1441447125103169654370228, 'val': 1}
  • id: 42219
    {'lmfdb_iso': '1584.k', 'p': 29, 'prec': 20, 'unit': 1588635245458118313922838407, 'val': 1}
  • id: 42230
    {'lmfdb_iso': '1584.k', 'p': 31, 'prec': 20, 'unit': 249901495386314826134821672, 'val': 2}
  • id: 42215
    {'lmfdb_iso': '1584.k', 'p': 37, 'prec': 20, 'unit': 586647456184796338526496212409, 'val': 1}
  • id: 42217
    {'lmfdb_iso': '1584.k', 'p': 41, 'prec': 20, 'unit': 2325253378339466444760750336705, 'val': 1}
  • id: 42218
    {'lmfdb_iso': '1584.k', 'p': 43, 'prec': 20, 'unit': 562466005802269307033161262907, 'val': 1}
  • id: 42228
    {'lmfdb_iso': '1584.k', 'p': 47, 'prec': 20, 'unit': 4923900273608001498512840625466, 'val': 1}
  • id: 42224
    {'lmfdb_iso': '1584.k', 'p': 53, 'prec': 20, 'unit': 410168100292201990527753539172178, 'val': 1}
  • id: 42225
    {'lmfdb_iso': '1584.k', 'p': 59, 'prec': 20, 'unit': 52726010336192808091994147673365, 'val': 2}
  • id: 42229
    {'lmfdb_iso': '1584.k', 'p': 61, 'prec': 20, 'unit': 1778491953746236964000258199260725, 'val': 1}
  • id: 42214
    {'lmfdb_iso': '1584.k', 'p': 67, 'prec': 20, 'unit': 41425602800379021198190213481932984, 'val': 1}
  • id: 42227
    {'lmfdb_iso': '1584.k', 'p': 71, 'prec': 20, 'unit': 82103880780421999775324848713867474, 'val': 1}
  • id: 42226
    {'lmfdb_iso': '1584.k', 'p': 73, 'prec': 20, 'unit': 163831658539835976343043337494413161, 'val': 1}
  • id: 42221
    {'lmfdb_iso': '1584.k', 'p': 79, 'prec': 20, 'unit': 397659070387050735694697410035666982, 'val': 1}
  • id: 42213
    {'lmfdb_iso': '1584.k', 'p': 83, 'prec': 20, 'unit': 1864551567475080693113423976286507108, 'val': 1}
  • id: 42212
    {'lmfdb_iso': '1584.k', 'p': 97, 'prec': 20, 'unit': 41687456893578083638793987414153780164, 'val': 1}