Elliptic curve data - 48672.l2

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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': '48672s', 'Clabel': '48672s3', 'Cnumber': 3, 'abc_quality': 1.069422794221752, 'absD': 11114367774981599232, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 0, 0, -561756, 23130016], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 48672, 'degree': 1032192, 'elladic_images': ['8.12.0.13'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3444971654142045841199492881', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 2, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 4], 'jinv': [1360251712, 771147], 'lmfdb_iso': '48672.l', 'lmfdb_label': '48672.l2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -369, 513], 'min_quad_twist_disc': 156, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.6', '12.12.0.h.1', '24.24.0-12.h.1.5', '52.12.0-4.c.1.2', '104.24.0.?', '156.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.18043083821056393902164917260', 'prec': 107}, 'szpiro_ratio': 4.755928963561191, '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, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 6, 0, -8, 0], 'aplist': [0, 0, -2, 0, -4, 0, 6, -8, 8, -2, 8, 10, 6, 4, 0, 14, 12, -10, -8, 0, 14, 4, -4, -10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 48672, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '48672.l', 'trace_hash': 1738240423486171852}
• 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': '0.0091959295704303837818750583879', 'prec': 110}, 'conductor': 48672, 'gens': [], 'heights': [], 'lmfdb_label': '48672.l2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.19545807696116411714593390202', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5636646156893129371674712161845225190', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[728, 0, 1]], 'xcoord_integral_points': [728]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '48672.l2'}
• ec_torsion_growth •

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

  
  
  • id: 2369852
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '48672.l2', 'torsion': [4]}
  • id: 2369851
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '48672.l2', 'torsion': [4]}
  • id: 2369850
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '48672.l2', 'torsion': [2, 2]}
  • id: 2369853
    {'degree': 4, 'field': [-3, 12, -11, -2, 1], 'lmfdb_label': '48672.l2', 'torsion': [2, 4]}
  • id: 2369857
    {'degree': 8, 'field': [-9087, -11856, 4614, 2076, 288, -108, -2, -4, 1], 'lmfdb_label': '48672.l2', 'torsion': [6]}
  • id: 2369855
    {'degree': 8, 'field': [81, 0, -270, 0, 165, 0, -30, 0, 1], 'lmfdb_label': '48672.l2', 'torsion': [8]}
  • id: 2369854
    {'degree': 8, 'field': [286, 468, 322, 96, 51, -12, 10, 0, 1], 'lmfdb_label': '48672.l2', 'torsion': [2, 4]}
  • id: 2369856
    {'degree': 8, 'field': [1225, 0, -272, 0, 30, 0, 16, 0, 1], 'lmfdb_label': '48672.l2', 'torsion': [8]}
  • id: 2369861
    {'degree': 16, 'field': [729, 0, -13296, 0, 41596, 0, -44640, 0, 11502, 0, 3728, 0, 588, 0, 0, 0, 1], 'lmfdb_label': '48672.l2', 'torsion': [2, 6]}
  • id: 2369860
    {'degree': 16, 'field': [841, 7424, 8372, -38832, -32200, 81568, 21796, -63528, -4214, 22368, -428, -3760, 248, 288, -28, -8, 1], 'lmfdb_label': '48672.l2', 'torsion': [2, 8]}
  • id: 2369859
    {'degree': 16, 'field': [5625, -9000, 13500, -16320, 7864, -4632, 12108, -13192, 5114, 920, -1540, 416, 120, -120, 44, -8, 1], 'lmfdb_label': '48672.l2', 'torsion': [2, 8]}
  • id: 2369858
    {'degree': 16, 'field': [22932, 58968, 42156, 24840, 47982, 25704, 12018, 10008, 6697, 492, 2158, -96, 336, -12, 28, 0, 1], 'lmfdb_label': '48672.l2', 'torsion': [4, 4]}
  • id: 2369862
    {'degree': 16, 'field': [59049, 0, 215784, 0, 243000, 0, 149904, 0, 25494, 0, 2232, 0, -456, 0, -16, 0, 1], 'lmfdb_label': '48672.l2', 'torsion': [12]}
  • id: 2369863
    {'degree': 16, 'field': [2390116, 0, -1906928, 0, -201452, 0, -44068, 0, 12113, 0, 6224, 0, 874, 0, 52, 0, 1], 'lmfdb_label': '48672.l2', '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: 1163278
    {'conductor': 48672, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '48672.l2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1163279
    {'conductor': 48672, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '48672.l2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1163280
    {'conductor': 48672, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '48672.l2', 'prime': 13, '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: 1988199
    {'adelic_gens': [[7, 6, 306, 307], [1, 0, 8, 1], [1, 8, 0, 1], [203, 198, 122, 275], [1, 4, 4, 17], [100, 311, 185, 306], [192, 31, 47, 60], [305, 8, 304, 9], [167, 304, 44, 279]], 'adelic_image': '312.48.0.?', 'conductor': 48672, 'lmfdb_label': '48672.l2', 'prime': 0}
  • id: 209857
    {'conductor': 48672, 'elladic_image': '8.12.0.13', 'lmfdb_label': '48672.l2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 48672.l does not appear in ec_padic