Elliptic curve data - 291312.bw1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '291312bw', 'Clabel': '291312bw4', 'Cnumber': 4, 'abc_quality': 0.9500550123380991, 'absD': 31603559036901110784, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2856, 'ainvs': [0, 0, 0, -1415811, -589314350], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 291312, 'degree': 5898240, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4777862483027286328188202338', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 48, 'isogeny_degrees': [1, 2, 4], 'jinv': [17418812548, 1753941], 'lmfdb_iso': '291312.bw', 'lmfdb_label': '291312.bw1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -544, -4624], 'min_quad_twist_disc': 204, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.3', '42.6.0.a.1', '56.12.0-4.c.1.3', '84.12.0.?', '136.12.0.?', '168.24.0.?', '204.12.0.?', '408.24.0.?', '476.12.0.?', '952.24.0.?', '1428.24.0.?', '2856.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.7950728806854000654367976397', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.065749218526055344184596461478', 'prec': 110}, 'szpiro_ratio': 4.299999734066008, '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, -2, 0, 1, 0, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, -2, 1, 4, 6, 0, 0, 0, 2, 0, -6, 2, -4, 0, 2, -4, -2, -4, 0, -14, 8, 12, 6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 291312, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '291312.bw', 'trace_hash': 264217128599492032}
• 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': '0.0070440464323887552552480595859', 'prec': 110}, 'conductor': 291312, 'gens': [[7769, 676260, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.7950728806854000654367976397', 'prec': 100}], 'lmfdb_label': '291312.bw1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.13930201089710459217348299302', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.4585805404886994506463767568447134950', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-850, 0, 1]], 'xcoord_integral_points': [-850, 7769]}
• lmfdb_label 291312.bw1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12363799
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '291312.bw1', 'torsion': [2, 2]}
  • id: 12363800
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '291312.bw1', 'torsion': [4]}
  • id: 12363801
    {'degree': 2, 'field': [30, -1, 1], 'lmfdb_label': '291312.bw1', 'torsion': [4]}
  • id: 12363802
    {'degree': 4, 'field': [60, -54, 19, -1, 1], 'lmfdb_label': '291312.bw1', 'torsion': [2, 4]}
  • id: 12363804
    {'degree': 8, 'field': [25, -30, 46, -26, -1, 14, 0, -4, 1], 'lmfdb_label': '291312.bw1', 'torsion': [8]}
  • id: 12363806
    {'degree': 8, 'field': [391, -3094, 3094, -2312, 884, -170, 4, -4, 1], 'lmfdb_label': '291312.bw1', 'torsion': [6]}
  • id: 12363805
    {'degree': 8, 'field': [7056, 0, 3528, 0, 1680, 0, 42, 0, 1], 'lmfdb_label': '291312.bw1', 'torsion': [8]}
  • id: 12363803
    {'degree': 8, 'field': [259081, 0, -213350, 0, 11919, 0, -170, 0, 1], 'lmfdb_label': '291312.bw1', 'torsion': [2, 4]}
  • id: 12363810
    {'degree': 16, 'field': [-387904401, 72557082, 79015170, 59590320, -27360932, -16479570, 4794516, 2370100, -463509, -206118, 28104, 2712, 1860, -344, -48, 0, 1], 'lmfdb_label': '291312.bw1', 'torsion': [2, 6]}
  • id: 12363809
    {'degree': 16, 'field': [270925, -188880, 374138, -305402, 361581, -181944, 126228, -55850, 28404, -8934, 2860, -912, 329, -50, 10, -4, 1], 'lmfdb_label': '291312.bw1', 'torsion': [2, 8]}
  • id: 12363808
    {'degree': 16, 'field': [10694800, 14260000, 182309024, -121241904, 60855788, 43462664, -28422884, -9583176, 4579255, 850020, -317156, -33152, 10577, 588, -166, -4, 1], 'lmfdb_label': '291312.bw1', 'torsion': [2, 8]}
  • id: 12363807
    {'degree': 16, 'field': [56307213, -197402436, 182894652, 10479672, -28359273, -3712548, 20358, 926016, 240112, -71316, -21248, 2184, 2199, -84, -74, 0, 1], 'lmfdb_label': '291312.bw1', 'torsion': [4, 4]}
  • id: 12363812
    {'degree': 16, 'field': [259822161, 0, 107544672, 0, 38749356, 0, 3259008, 0, 212598, 0, 13344, 0, 396, 0, 0, 0, 1], 'lmfdb_label': '291312.bw1', 'torsion': [12]}
  • id: 12363811
    {'degree': 16, 'field': [732524953, -568180712, 713362284, -311517384, 210652122, -71617512, 33823300, -9294464, 3314079, -713952, 197940, -32016, 6974, -784, 132, -8, 1], 'lmfdb_label': '291312.bw1', 'torsion': [12]}
• 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: 7217240
    {'conductor': 291312, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '291312.bw1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 7217241
    {'conductor': 291312, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '291312.bw1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7217242
    {'conductor': 291312, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '291312.bw1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 7217243
    {'conductor': 291312, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '291312.bw1', 'prime': 17, '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: 3499098
    {'adelic_gens': [[167, 2848, 668, 2823], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1636, 1, 839, 6], [7, 6, 2850, 2851], [1900, 2855, 929, 2850], [2849, 8, 2848, 9], [1075, 1074, 370, 1795], [1781, 1784, 334, 1779]], 'adelic_image': '2856.48.0.?', 'conductor': 291312, 'lmfdb_label': '291312.bw1', 'prime': 0}
  • id: 1031426
    {'conductor': 291312, 'elladic_image': '4.6.0.1', 'lmfdb_label': '291312.bw1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 291312.bw does not appear in ec_padic