Elliptic curve data - 1584.o1

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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': '1584q', 'Clabel': '1584q3', 'Cnumber': 3, 'abc_quality': 1.0091329432672695, 'absD': 1180380377088, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [0, 0, 0, -21099, 1178458], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1584, 'degree': 3072, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2298212577773115568724086197', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 4], 'jinv': [347873904937, 395307], 'lmfdb_iso': '1584.o', 'lmfdb_label': '1584.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -146, 621], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '12.24.0-12.h.1.2', '88.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 6, 176], [11, 12, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.012632067116688598242446120220', 'prec': 110}, 'szpiro_ratio': 5.630589945319043, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 2, 0, -4, 0, 0, 0, 1, 0, -2, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, 2, -4, 1, -2, 2, 0, 8, 6, 8, 6, 2, 0, 8, -6, -4, 6, 4, 0, -14, 4, 12, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 1584, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1584.o', 'trace_hash': 1619252262249239878}
• 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': '0.085465498093119428952841327091', 'prec': 107}, 'conductor': 1584, 'gens': [], 'heights': [], 'lmfdb_label': '1584.o1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.86295291625043705745817375995', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7259058325008741149163475198928141737', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[119, 594, 1]], 'xcoord_integral_points': [86, 119]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '11': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1584.o1'}
• ec_torsion_growth •

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

  
  
  • id: 78742
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1584.o1', 'torsion': [2, 4]}
  • id: 78743
    {'degree': 4, 'field': [48, 0, -18, 0, 1], 'lmfdb_label': '1584.o1', 'torsion': [8]}
  • id: 78747
    {'degree': 8, 'field': [-3, 0, 0, 0, 6, 0, 5, 0, 1], 'lmfdb_label': '1584.o1', 'torsion': [12]}
  • id: 78744
    {'degree': 8, 'field': [9, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '1584.o1', 'torsion': [4, 4]}
  • id: 78746
    {'degree': 8, 'field': [36, 0, -252, 0, 165, 0, -24, 0, 1], 'lmfdb_label': '1584.o1', 'torsion': [2, 8]}
  • id: 78745
    {'degree': 8, 'field': [253, -242, 146, -2, -5, 2, 8, -4, 1], 'lmfdb_label': '1584.o1', 'torsion': [2, 8]}
  • id: 78749
    {'degree': 16, 'field': [9, 0, -99, 0, 180, 0, -162, 0, 120, 0, -72, 0, 25, 0, -5, 0, 1], 'lmfdb_label': '1584.o1', 'torsion': [2, 12]}
  • id: 78748
    {'degree': 16, 'field': [278784, 0, -1254528, 0, 762696, 0, -38808, 0, -27543, 0, -4536, 0, 864, 0, -48, 0, 1], 'lmfdb_label': '1584.o1', 'torsion': [16]}
• 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: 24565
    {'conductor': 1584, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '1584.o1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 24566
    {'conductor': 1584, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '1584.o1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 24567
    {'conductor': 1584, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1584.o1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1674364
    {'adelic_gens': [[80, 261, 83, 262], [235, 234, 178, 43], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 258, 259], [32, 157, 29, 0], [257, 8, 256, 9], [145, 8, 52, 33]], 'adelic_image': '264.48.0.?', 'conductor': 1584, 'lmfdb_label': '1584.o1', 'prime': 0}
  • id: 7598
    {'conductor': 1584, 'elladic_image': '4.12.0.7', 'lmfdb_label': '1584.o1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1584.o does not appear in ec_padic