Elliptic curve data - 12495.b5

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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': '12495a', 'Clabel': '12495a1', 'Cnumber': 1, 'abc_quality': 0.8766842762334948, 'absD': 2296387889775, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 28560, 'ainvs': [1, 1, 1, 1714, -66886], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 12495, 'degree': 24576, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0544847479122060419920117099', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4733169839, 19518975], 'lmfdb_iso': '12495.b', 'lmfdb_label': '12495.b5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 35, 200], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '28.12.0-4.c.1.2', '40.24.0-8.n.1.8', '48.24.0-8.n.1.5', '56.24.0-8.n.1.5', '68.12.0-4.c.1.2', '136.24.0.?', '238.6.0.?', '240.48.0.?', '280.48.0.?', '336.48.0.?', '476.24.0.?', '680.48.0.?', '816.48.0.?', '952.48.0.?', '1680.96.0.?', '4080.96.0.?', '4760.96.0.?', '5712.96.0.?', '28560.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.081529673384549389439335338178', 'prec': 107}, 'szpiro_ratio': 3.7915354166032116, '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, -1, 1, 0, 3, 1, 1, 4, 1, -6, 0, 1, -1, -1, -1, 4, 1], 'aplist': [-1, -1, -1, 0, 4, -6, -1, 4, 0, 6, 8, -2, 6, 4, 0, -10, -12, 2, 12, 16, -10, 16, -4, 14, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 12495, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '12495.b', 'trace_hash': 1043496155389508941}
• 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': '0.12136296705980287413271113722', 'prec': 103}, 'conductor': 12495, 'gens': [], 'heights': [], 'lmfdb_label': '12495.b5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.41489364987470476384484951437', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.82978729974940952768969902874549958161', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[27, -14, 1]], 'xcoord_integral_points': [27]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [0, 0], '5': [0, 0], '7': 'a', '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '12495.b5'}
• ec_torsion_growth •

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

  
  
  • id: 645533
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '12495.b5', 'torsion': [4]}
  • id: 645534
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '12495.b5', 'torsion': [4]}
  • id: 645532
    {'degree': 2, 'field': [30, -1, 1], 'lmfdb_label': '12495.b5', 'torsion': [2, 2]}
  • id: 645536
    {'degree': 4, 'field': [4, 2, 5, -1, 1], 'lmfdb_label': '12495.b5', 'torsion': [8]}
  • id: 645535
    {'degree': 4, 'field': [36, 0, -5, 0, 1], 'lmfdb_label': '12495.b5', 'torsion': [2, 4]}
  • id: 645537
    {'degree': 4, 'field': [529, 0, -39, 0, 1], 'lmfdb_label': '12495.b5', 'torsion': [8]}
  • id: 645541
    {'degree': 8, 'field': [-145, 472, -490, 35, -14, -7, 7, -4, 1], 'lmfdb_label': '12495.b5', 'torsion': [6]}
  • id: 645539
    {'degree': 8, 'field': [548, 668, -714, 98, -63, 14, 0, -4, 1], 'lmfdb_label': '12495.b5', 'torsion': [8]}
  • id: 645540
    {'degree': 8, 'field': [1556, 750, -223, -218, 104, 2, -6, -2, 1], 'lmfdb_label': '12495.b5', 'torsion': [2, 8]}
  • id: 645538
    {'degree': 8, 'field': [51956, 56824, 23936, 3776, 573, 278, 34, -2, 1], 'lmfdb_label': '12495.b5', 'torsion': [2, 4]}
  • id: 645543
    {'degree': 16, 'field': [6561, 0, 0, 0, 22194, 0, 0, 0, 1795, 0, 0, 0, 274, 0, 0, 0, 1], 'lmfdb_label': '12495.b5', 'torsion': [2, 8]}
  • id: 645548
    {'degree': 16, 'field': [540225, 0, 617400, 0, 176400, 0, 68257, 0, 23912, 0, -497, 0, 49, 0, 14, 0, 1], 'lmfdb_label': '12495.b5', 'torsion': [12]}
  • id: 645547
    {'degree': 16, 'field': [4004001, 0, -6529284, 0, 1472184, 0, 82033, 0, -16744, 0, -5537, 0, 469, 0, -34, 0, 1], 'lmfdb_label': '12495.b5', 'torsion': [12]}
  • id: 645546
    {'degree': 16, 'field': [18643641, -12276270, 8271181, -5109805, 4193698, -1656424, 1460215, -412141, 265319, -57818, 28763, -4819, 1912, -217, 67, -4, 1], 'lmfdb_label': '12495.b5', 'torsion': [2, 6]}
  • id: 645542
    {'degree': 16, 'field': [146410000, 0, 0, 0, 52724200, 0, 0, 0, 491361, 0, 0, 0, 1702, 0, 0, 0, 1], 'lmfdb_label': '12495.b5', 'torsion': [4, 4]}
  • id: 645544
    {'degree': 16, 'field': [180660481, -165122685, 41879568, 7702695, -4055020, -395010, 529023, -133560, -5406, 12285, -1248, -630, 185, 0, -18, 0, 1], 'lmfdb_label': '12495.b5', 'torsion': [16]}
  • id: 645545
    {'degree': 16, 'field': [5195796781, -5018607146, 3225028709, -1751475376, 507886621, 16168272, -42480574, 3433832, 3550627, -1614362, 418436, -63192, 1096, 1216, -136, -4, 1], 'lmfdb_label': '12495.b5', '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: 270770
    {'conductor': 12495, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '12495.b5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 270771
    {'conductor': 12495, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12495.b5', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 270772
    {'conductor': 12495, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '12495.b5', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 270773
    {'conductor': 12495, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12495.b5', 'prime': 17, '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: 1746984
    {'adelic_gens': [[9521, 16, 19048, 129], [15, 2, 28462, 28547], [10088, 1, 6799, 10], [1, 16, 7148, 7269], [28545, 16, 28544, 17], [1, 16, 0, 1], [16304, 28555, 4125, 14], [5, 4, 28556, 28557], [22861, 16, 11168, 28245], [1, 0, 16, 1], [10721, 16, 3506, 21327]], 'adelic_image': '28560.192.1.?', 'conductor': 12495, 'lmfdb_label': '12495.b5', 'prime': 0}
  • id: 59594
    {'conductor': 12495, 'elladic_image': '8.12.0.5', 'lmfdb_label': '12495.b5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 12495.b does not appear in ec_padic