Elliptic curve data - 12495.b4

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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': '12495a2', 'Cnumber': 2, 'abc_quality': 0.9800332334775532, 'absD': 84342641630625, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 14280, 'ainvs': [1, 1, 1, -18131, -836872], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 12495, 'degree': 49152, 'elladic_images': ['4.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4010583381921786967006277707', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [5602762882081, 716900625], 'lmfdb_iso': '12495.b', 'lmfdb_label': '12495.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -370, 2387], 'min_quad_twist_disc': -7, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '24.24.0-4.b.1.3', '28.24.0-4.b.1.3', '40.24.0-4.b.1.3', '68.24.0-4.b.1.2', '120.48.0.?', '168.48.0.?', '280.48.0.?', '408.48.0.?', '476.48.0.?', '680.48.0.?', '840.96.0.?', '2040.96.0.?', '2856.96.0.?', '4760.96.0.?', '14280.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.42810326366452204414795139898', 'prec': 103}, 'szpiro_ratio': 4.349557635641127, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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': '0.060681483529901437066355568608', 'prec': 107}, 'conductor': 12495, 'gens': [], 'heights': [], 'lmfdb_label': '12495.b4', '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': 32, 'torsion_generators': [[-99, 49, 1], [153, -77, 1]], 'xcoord_integral_points': [-99, 153]}
• 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.b4'}
• ec_torsion_growth •

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

  
  
  • id: 645549
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '12495.b4', 'torsion': [2, 4]}
  • id: 645550
    {'degree': 4, 'field': [2, 22, -21, -2, 1], 'lmfdb_label': '12495.b4', 'torsion': [2, 4]}
  • id: 645551
    {'degree': 4, 'field': [36, 0, 5, 0, 1], 'lmfdb_label': '12495.b4', 'torsion': [2, 4]}
  • id: 645555
    {'degree': 8, 'field': [-145, 472, -490, 35, -14, -7, 7, -4, 1], 'lmfdb_label': '12495.b4', 'torsion': [2, 6]}
  • id: 645554
    {'degree': 8, 'field': [16, 8, -16, 18, 23, -9, -4, -1, 1], 'lmfdb_label': '12495.b4', 'torsion': [2, 8]}
  • id: 645552
    {'degree': 8, 'field': [72, -288, 470, -390, 261, -82, 32, -4, 1], 'lmfdb_label': '12495.b4', 'torsion': [4, 4]}
  • id: 645553
    {'degree': 8, 'field': [19429, 2446, -1336, -2162, 937, 170, -52, -4, 1], 'lmfdb_label': '12495.b4', 'torsion': [2, 8]}
  • id: 645558
    {'degree': 16, 'field': [540225, 0, 617400, 0, 176400, 0, 68257, 0, 23912, 0, -497, 0, 49, 0, 14, 0, 1], 'lmfdb_label': '12495.b4', 'torsion': [2, 12]}
  • id: 645557
    {'degree': 16, 'field': [8850625, 0, 14161000, 0, 9091600, 0, 2384760, 0, 242526, 0, 8760, 0, 1552, 0, 40, 0, 1], 'lmfdb_label': '12495.b4', 'torsion': [2, 8]}
  • id: 645556
    {'degree': 16, 'field': [17348368, 23351360, -16160624, -14550928, 7758884, -729400, 438984, -65908, -102199, 65932, -840, -5684, 98, 364, -32, -8, 1], 'lmfdb_label': '12495.b4', '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: 270774
    {'conductor': 12495, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12495.b4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 270775
    {'conductor': 12495, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12495.b4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 270776
    {'conductor': 12495, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '12495.b4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 270777
    {'conductor': 12495, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12495.b4', 'prime': 17, 'reduction_type': -1, '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: 1746983
    {'adelic_gens': [[3, 10718, 28, 3645], [1687, 2, 5862, 14275], [1, 0, 8, 1], [14273, 8, 14272, 9], [1, 8, 0, 1], [2857, 8, 11428, 33], [14273, 14274, 8166, 5], [9521, 4, 0, 1], [5, 4, 14276, 14277], [7145, 3576, 3564, 7133]], 'adelic_image': '14280.192.1.?', 'conductor': 12495, 'lmfdb_label': '12495.b4', 'prime': 0}
  • id: 59593
    {'conductor': 12495, 'elladic_image': '4.12.0.3', 'lmfdb_label': '12495.b4', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 12495.b does not appear in ec_padic