Elliptic curve data - 1248.e2

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

  
  {'Ciso': '1248f', 'Clabel': '1248f2', 'Cnumber': 2, 'abc_quality': 1.0253733958534896, 'absD': 1601419382784, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 104, 'ainvs': [0, -1, 0, -2497, 78385], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1248, 'degree': 1536, 'elladic_images': ['8.12.0.37'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0383696677566685057230846201', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [-420526439488, 390971529], 'lmfdb_iso': '1248.e', 'lmfdb_label': '1248.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -2497, 78385], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '8.12.0-4.a.1.1', '52.12.0.d.1', '104.48.0.?'], '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, 'serre_invariants': [[2, 2, 1], [3, 4, 32], [13, 14, 96]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.34522248719672319630585249864', 'prec': 103}, 'szpiro_ratio': 5.0552762721469495, '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, -1, 0, 2, 0, -2, 0, 1, 0, 2, 0, -1, 0, -2, 0, 6, 0, -2, 0], 'aplist': [0, -1, 2, -2, 2, -1, 6, -2, 0, 2, 2, 10, 2, 8, -2, -2, 10, 6, 14, -14, -6, -4, 6, 10, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 1248, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1248.e', 'trace_hash': 848164726588554476}
• 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': '0.12533823255204411042883992923', 'prec': 103}, 'conductor': 1248, 'gens': [], 'heights': [], 'lmfdb_label': '1248.e2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.77076490601717157141159448558', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5415298120343431428231889711636757596', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-61, 0, 1]], 'xcoord_integral_points': [-61]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '1248.e2'}
• ec_torsion_growth •

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

  
  
  • id: 62035
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1248.e2', 'torsion': [2, 2]}
  • id: 62036
    {'degree': 4, 'field': [-1, 0, -3, 0, 1], 'lmfdb_label': '1248.e2', 'torsion': [4]}
  • id: 62039
    {'degree': 8, 'field': [-3, 0, 40, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '1248.e2', 'torsion': [6]}
  • id: 62038
    {'degree': 8, 'field': [1, 0, 2, -12, 20, -12, 2, 0, 1], 'lmfdb_label': '1248.e2', 'torsion': [2, 4]}
  • id: 62037
    {'degree': 8, 'field': [9, -6, 2, -10, 7, -6, 8, -4, 1], 'lmfdb_label': '1248.e2', 'torsion': [2, 4]}
  • id: 62040
    {'degree': 16, 'field': [1, -8, 50, -144, 226, -136, -174, 340, -21, -380, 318, -28, -56, 0, 20, -8, 1], 'lmfdb_label': '1248.e2', 'torsion': [4, 4]}
  • id: 62042
    {'degree': 16, 'field': [4, -16, 32, -16, -48, 152, -192, 80, 148, -312, 328, -256, 164, -84, 32, -8, 1], 'lmfdb_label': '1248.e2', 'torsion': [2, 6]}
  • id: 62041
    {'degree': 16, 'field': [729, 0, -5688, 0, -7672, 0, -2432, 0, 710, 0, 792, 0, 232, 0, 32, 0, 1], 'lmfdb_label': '1248.e2', 'torsion': [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: 18518
    {'conductor': 1248, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '1248.e2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 18519
    {'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1248.e2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 18520
    {'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '1248.e2', 'prime': 13, '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: 1672421
    {'adelic_gens': [[97, 8, 96, 9], [5, 8, 48, 77], [53, 4, 2, 9], [1, 0, 8, 1], [3, 8, 10, 27], [41, 2, 0, 1], [77, 100, 39, 103], [1, 8, 0, 1]], 'adelic_image': '104.48.0.?', 'conductor': 1248, 'lmfdb_label': '1248.e2', 'prime': 0}
  • id: 5980
    {'conductor': 1248, 'elladic_image': '8.12.0.37', 'lmfdb_label': '1248.e2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1248.e does not appear in ec_padic