Elliptic curve data - 72897.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
  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': '72897a', 'Clabel': '72897a3', 'Cnumber': 3, 'abc_quality': 1.0376318384434067, 'absD': 63013686710249979, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 12408, 'ainvs': [1, 1, 0, 96046, -3781845], 'analytic_rank': 0, 'bad_primes': [3, 11, 47], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 72897, 'degree': 618240, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9124417337383406951680292147', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [9090072503, 5845851], 'lmfdb_iso': '72897.a', 'lmfdb_label': '72897.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 44, 55], 'min_quad_twist_disc': -47, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '22.6.0.a.1', '24.12.0.ba.1', '44.12.0.g.1', '188.12.0.?', '264.24.0.?', '1128.24.0.?', '2068.24.0.?', '12408.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 24299], [3, 4, 24299], [11, 12, 6627], [47, 1106, 33]], 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.012632067116688598242446120187', 'prec': 110}, 'szpiro_ratio': 4.111114154466234, '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, 1, -1, -1, 2, -1, 4, -3, 1, 2, -1, 1, 2, 4, -2, -1, -2, 1, 0, -2], 'aplist': [1, -1, 2, 4, -1, 2, -2, 0, -8, 6, 8, 6, 2, 0, 0, 6, -4, 6, 4, 0, 14, -4, 12, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 72897, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '72897.a', 'trace_hash': 1112042533151514900}
• 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': '0.021820978236541130796470126066', 'prec': 107}, 'conductor': 72897, 'gens': [], 'heights': [], 'lmfdb_label': '72897.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20017296067580021634627815832', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6031132921644038942330068497115530484', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[155, -155, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 2], '3': [2, 0], '11': [0, 0], '47': 'a'}, 'iwp0': 5, 'lmfdb_label': '72897.a4'}
• ec_torsion_growth •

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

  
  
  • id: 3454363
    {'degree': 2, 'field': [-47, 0, 1], 'lmfdb_label': '72897.a4', 'torsion': [4]}
  • id: 3454362
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '72897.a4', 'torsion': [2, 2]}
  • id: 3454364
    {'degree': 2, 'field': [517, 0, 1], 'lmfdb_label': '72897.a4', 'torsion': [4]}
  • id: 3454365
    {'degree': 4, 'field': [2453, 88, -87, -2, 1], 'lmfdb_label': '72897.a4', 'torsion': [2, 4]}
  • id: 3454369
    {'degree': 8, 'field': [-95903, -50006, -25130, 3027, -933, 111, -2, -2, 1], 'lmfdb_label': '72897.a4', 'torsion': [6]}
  • id: 3454367
    {'degree': 8, 'field': [-3707, 11484, -7668, -504, 1109, -36, -66, 0, 1], 'lmfdb_label': '72897.a4', 'torsion': [8]}
  • id: 3454366
    {'degree': 8, 'field': [23508, -5372, 6258, -1820, 1031, -148, 54, -4, 1], 'lmfdb_label': '72897.a4', 'torsion': [2, 4]}
  • id: 3454368
    {'degree': 8, 'field': [275659609, 0, 10764656, 0, 125622, 0, 608, 0, 1], 'lmfdb_label': '72897.a4', 'torsion': [8]}
  • id: 3454370
    {'degree': 16, 'field': [276922881, 0, 231154128, 0, 73807618, 0, 12810384, 0, 1373795, 0, 93648, 0, 3974, 0, 96, 0, 1], 'lmfdb_label': '72897.a4', 'torsion': [4, 4]}
  • id: 3454374
    {'degree': 16, 'field': [378341401, 0, -243944803, 0, 71871412, 0, -12313707, 0, 1322697, 0, -90717, 0, 3871, 0, -94, 0, 1], 'lmfdb_label': '72897.a4', 'torsion': [12]}
  • id: 3454372
    {'degree': 16, 'field': [765766948, 446660184, -137462852, -55076520, 41922026, -633312, -9549498, 363528, 1175081, -14268, -85878, 0, 3836, -12, -92, 0, 1], 'lmfdb_label': '72897.a4', 'torsion': [2, 8]}
  • id: 3454373
    {'degree': 16, 'field': [23015602731, 18125183670, 407176421, -2813539825, -47654434, 276748242, 1079403, -12884346, 746776, 426931, -6677, -5023, 284, 272, 7, -2, 1], 'lmfdb_label': '72897.a4', 'torsion': [2, 6]}
  • id: 3454375
    {'degree': 16, 'field': [134121148153, -61751332390, 11851417803, 5685573698, 454419289, 139801056, 47716614, -2739930, 2656335, -393318, 114153, -3528, -161, 230, 0, -4, 1], 'lmfdb_label': '72897.a4', 'torsion': [12]}
  • id: 3454371
    {'degree': 16, 'field': [65533347801289, 0, 7134782092144, 0, 294533888030, 0, 6238091964, 0, 97101311, 0, 1494804, 0, 15182, 0, 100, 0, 1], 'lmfdb_label': '72897.a4', 'torsion': [2, 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: 1768629
    {'conductor': 72897, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '72897.a4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1768630
    {'conductor': 72897, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '72897.a4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1768631
    {'conductor': 72897, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '72897.a4', 'prime': 47, 'reduction_type': 0, '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: 2145921
    {'adelic_gens': [[11087, 0, 0, 12407], [11140, 8977, 10199, 7662], [1, 0, 8, 1], [12401, 8, 12400, 9], [3667, 10528, 3290, 9213], [3667, 3666, 9682, 4795], [8273, 9776, 6956, 1881], [7, 6, 12402, 12403], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '12408.48.0.?', 'conductor': 72897, 'lmfdb_label': '72897.a4', 'prime': 0}
  • id: 302468
    {'conductor': 72897, 'elladic_image': '4.6.0.1', 'lmfdb_label': '72897.a4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 72897.a does not appear in ec_padic