Elliptic curve data - 72897.a3

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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': '72897a1', 'Cnumber': 1, 'abc_quality': 1.0970565641289056, 'absD': 3201426952713, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 12408, 'ainvs': [1, 1, 0, -14404, 653827], 'analytic_rank': 0, 'bad_primes': [3, 11, 47], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 72897, 'degree': 154560, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2192945531783953857507970932', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [30664297, 297], 'lmfdb_iso': '72897.a', 'lmfdb_label': '72897.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -6, -9], 'min_quad_twist_disc': -47, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '66.6.0.a.1', '88.12.0.?', '132.12.0.?', '264.24.0.?', '376.12.0.?', '564.12.0.?', '1128.24.0.?', '2068.12.0.?', '4136.24.0.?', '6204.24.0.?', '12408.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 4, 24299], [11, 12, 6627], [47, 1106, 33]], 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.70577924767663390765967824169', 'prec': 107}, 'szpiro_ratio': 3.6027691144463394, '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': '0.087283912946164523185880504263', 'prec': 107}, 'conductor': 72897, 'gens': [], 'heights': [], 'lmfdb_label': '72897.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.80069184270320086538511263327', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6031132921644038942330068497115530484', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[74, -37, 1]], 'xcoord_integral_points': [74]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 0], '3': [2, 0], '11': [0, 0], '47': 'a'}, 'iwp0': 5, 'lmfdb_label': '72897.a3'}
• ec_torsion_growth •

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

  
  
  • id: 3454342
    {'degree': 2, 'field': [-129, -1, 1], 'lmfdb_label': '72897.a3', 'torsion': [4]}
  • id: 3454341
    {'degree': 2, 'field': [-35, -1, 1], 'lmfdb_label': '72897.a3', 'torsion': [4]}
  • id: 3454340
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '72897.a3', 'torsion': [2, 2]}
  • id: 3454343
    {'degree': 4, 'field': [333, 237, -86, -1, 1], 'lmfdb_label': '72897.a3', 'torsion': [2, 4]}
  • id: 3454347
    {'degree': 8, 'field': [-95903, -50006, -25130, 3027, -933, 111, -2, -2, 1], 'lmfdb_label': '72897.a3', 'torsion': [6]}
  • id: 3454345
    {'degree': 8, 'field': [628, 9220, -3958, -2102, 817, 158, -52, -4, 1], 'lmfdb_label': '72897.a3', 'torsion': [8]}
  • id: 3454346
    {'degree': 8, 'field': [25292, -2006, 6533, -754, 852, -70, 46, -2, 1], 'lmfdb_label': '72897.a3', 'torsion': [8]}
  • id: 3454344
    {'degree': 8, 'field': [387766, 271046, 148109, 23768, 7816, 136, 158, -2, 1], 'lmfdb_label': '72897.a3', 'torsion': [2, 4]}
  • id: 3454349
    {'degree': 16, 'field': [34152336, 0, -62250228, 0, 39416289, 0, -11186712, 0, 1612552, 0, -125870, 0, 5352, 0, -116, 0, 1], 'lmfdb_label': '72897.a3', 'torsion': [2, 8]}
  • id: 3454350
    {'degree': 16, 'field': [639685264, -50735752, -161208600, 25035138, 19618781, -3278098, -2811156, 129352, 355338, -5344, -22734, -566, 1124, 48, -42, -2, 1], 'lmfdb_label': '72897.a3', 'torsion': [2, 8]}
  • id: 3454353
    {'degree': 16, 'field': [926649639, 3719668959, 4186010367, 755890002, 789297606, 77455629, 50911632, 10758180, -264495, 307860, -74096, -1038, -2628, -372, 3, 0, 1], 'lmfdb_label': '72897.a3', 'torsion': [12]}
  • id: 3454352
    {'degree': 16, 'field': [5639559409, -4209337044, 209766893, 366304279, -25549940, -6021925, -4134601, 607048, -100163, 93563, 7382, -11510, 844, 434, -55, -6, 1], 'lmfdb_label': '72897.a3', 'torsion': [12]}
  • id: 3454351
    {'degree': 16, 'field': [5922411433, -3501153995, 4481617494, -1973488221, 1018804743, -40258260, 16225318, -2056352, 58350, 334695, -97761, 16734, -2698, -70, 30, -8, 1], 'lmfdb_label': '72897.a3', 'torsion': [2, 6]}
  • id: 3454348
    {'degree': 16, 'field': [2585435669041, 0, -557878113940, 0, 53882175490, 0, -3021673060, 0, 106919203, 0, -2428300, 0, 34474, 0, -280, 0, 1], 'lmfdb_label': '72897.a3', 'torsion': [4, 4]}
• 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: 1768623
    {'conductor': 72897, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '72897.a3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1768624
    {'conductor': 72897, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '72897.a3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1768625
    {'conductor': 72897, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '72897.a3', 'prime': 47, '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: 2145920
    {'adelic_gens': [[11087, 0, 0, 12407], [1, 0, 8, 1], [1, 8, 0, 1], [7, 6, 12402, 12403], [1, 4, 4, 17], [12401, 8, 12400, 9], [10388, 8977, 12079, 7662], [6440, 2115, 6533, 8978], [11657, 564, 6110, 1223], [3667, 3666, 9682, 4795]], 'adelic_image': '12408.48.0.?', 'conductor': 72897, 'lmfdb_label': '72897.a3', 'prime': 0}
  • id: 302467
    {'conductor': 72897, 'elladic_image': '4.6.0.1', 'lmfdb_label': '72897.a3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 72897.a does not appear in ec_padic