Elliptic curve data - 456.d1

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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': '456b', 'Clabel': '456b3', 'Cnumber': 3, 'abc_quality': 0.9769218916313712, 'absD': 7206230016, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, 1, 0, -1272, 16560], 'analytic_rank': 0, 'bad_primes': [2, 3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 456, 'degree': 192, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.66620233886319334471104187522', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4], 'jinv': [111223479026, 3518667], 'lmfdb_iso': '456.d', 'lmfdb_label': '456.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1272, 16560], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.4', '12.12.0-4.c.1.1', '24.24.0-24.s.1.4', '152.24.0.?', '456.48.0.?'], '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, 4, 3], [3, 4, 152], [19, 20, 24]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.030817423349910144411912430550', 'prec': 107}, 'szpiro_ratio': 5.399667644130265, '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, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, -1, 0], 'aplist': [0, 1, 2, 0, 0, 2, 2, -1, 0, 2, -4, 2, 6, -4, 0, 10, -4, -2, -12, 0, -6, -4, -8, 6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 456, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '456.d', 'trace_hash': 276074583054395847}
• 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': '0.26384204277445476974974852732', 'prec': 103}, 'conductor': 456, 'gens': [], 'heights': [], 'lmfdb_label': '456.d1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.3176900889156274165731581927', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9765351333734411248597372890025863209', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [[23, 0, 1]], 'xcoord_integral_points': [23]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '19': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '456.d1'}
• ec_torsion_growth •

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

  
  
  • id: 20623
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [2, 2]}
  • id: 20624
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [4]}
  • id: 20625
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [4]}
  • id: 20626
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [2, 4]}
  • id: 20628
    {'degree': 8, 'field': [1, -6, -67, 0, 78, -6, -19, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [8]}
  • id: 20630
    {'degree': 8, 'field': [2, -92, 122, -54, 18, 0, 4, -4, 1], 'lmfdb_label': '456.d1', 'torsion': [6]}
  • id: 20627
    {'degree': 8, 'field': [36, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [2, 4]}
  • id: 20629
    {'degree': 8, 'field': [1764, 0, 240, 0, 34, 0, -16, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [8]}
  • id: 20631
    {'degree': 16, 'field': [81, 0, -324, 0, 648, 0, -864, 0, 711, 0, -288, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [4, 4]}
  • id: 20632
    {'degree': 16, 'field': [313, -1620, -1332, 9912, 2635, -21348, -5298, 19488, 6960, -7524, -3648, 936, 619, -36, -42, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [2, 8]}
  • id: 20636
    {'degree': 16, 'field': [576, 0, 1152, 0, 192, 0, -512, 0, 128, 0, -56, 0, -20, 0, -4, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [12]}
  • id: 20634
    {'degree': 16, 'field': [2916, 0, -29160, 0, -7020, 0, 2136, 0, 2940, 0, -492, 0, -92, 0, -2, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [2, 6]}
  • id: 20635
    {'degree': 16, 'field': [2916, 0, -1944, 0, -1620, 0, -756, 0, 288, 0, -192, 0, 12, 0, 12, 0, 1], 'lmfdb_label': '456.d1', 'torsion': [12]}
  • id: 20633
    {'degree': 16, 'field': [14641, 0, 23716, 0, 14240, 0, 4968, 0, 4871, 0, 1032, 0, 80, 0, 4, 0, 1], 'lmfdb_label': '456.d1', '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: 4942
    {'conductor': 456, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '456.d1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4943
    {'conductor': 456, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '456.d1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 4944
    {'conductor': 456, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '456.d1', 'prime': 19, '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: 1667822
    {'adelic_gens': [[97, 8, 388, 33], [160, 3, 157, 2], [449, 8, 448, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 450, 451], [400, 179, 403, 432], [288, 65, 163, 150]], 'adelic_image': '456.48.0.?', 'conductor': 456, 'lmfdb_label': '456.d1', 'prime': 0}
  • id: 2057
    {'conductor': 456, 'elladic_image': '8.12.0.8', 'lmfdb_label': '456.d1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 456.d does not appear in ec_padic