Elliptic curve data - 356928.dx2

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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': '356928dx', 'Clabel': '356928dx2', 'Cnumber': 2, 'abc_quality': 1.0349530577780537, 'absD': 151298672737428876435174457344, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 3432, 'ainvs': [0, -1, 0, -873083969, 21185794049601], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 356928, 'degree': 301916160, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.2882912645126073219149878063', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 101, 'isogeny_degrees': [1, 3], 'jinv': [-58169016237585194137, 119573538788081664], 'lmfdb_iso': '356928.dx', 'lmfdb_label': '356928.dx2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -80722, 18827108], 'min_quad_twist_disc': 104, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '66.8.0-3.a.1.2', '312.8.0.?', '1144.2.0.?', '3432.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1859], [3, 4, 118976], [11, 12, 32448], [13, 98, 2112]], 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.9660958149419209897623959033', 'prec': 100}, 'szpiro_ratio': 5.857655616407319, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 3, 0, 1, 0, 1, 0, 1, 0, 0, 0, -3, 0, 0, 0, 2, 0], 'aplist': [0, -1, 3, 1, 1, 0, 0, 2, 3, 3, -8, 2, 9, -5, 0, 6, -3, 1, 11, 6, 1, 2, 18, 0, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 356928, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '356928.dx', 'trace_hash': 2221446892364961184}
• 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': '0.00018846796187957650847137491422', 'prec': 113}, 'conductor': 356928, 'gens': [], 'heights': [], 'lmfdb_label': '356928.dx2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.028917378797288635785829881516', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1641025468095635531595029382484812367', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 356928.dx2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 14872716
    {'degree': 2, 'field': [78, 0, 1], 'lmfdb_label': '356928.dx2', 'torsion': [3]}
  • id: 14872717
    {'degree': 3, 'field': [2, 6, -1, 1], 'lmfdb_label': '356928.dx2', 'torsion': [2]}
  • id: 14872719
    {'degree': 6, 'field': [-7775, -15444, 2028, -198, -78, 0, 1], 'lmfdb_label': '356928.dx2', 'torsion': [3]}
  • id: 14872720
    {'degree': 6, 'field': [222, 276, 103, -24, -10, 0, 1], 'lmfdb_label': '356928.dx2', 'torsion': [6]}
  • id: 14872718
    {'degree': 6, 'field': [1144, 0, 289, 0, 34, 0, 1], 'lmfdb_label': '356928.dx2', 'torsion': [2, 2]}
  • id: 14872721
    {'degree': 12, 'field': [-124, 384, -434, 200, -256, 432, -265, 4, -35, -24, 13, -4, 1], 'lmfdb_label': '356928.dx2', 'torsion': [4]}
  • id: 14872723
    {'degree': 12, 'field': [350464, -42624, -31032, 52184, 6470, -3928, 2933, 230, -15, 36, 11, -2, 1], 'lmfdb_label': '356928.dx2', 'torsion': [2, 6]}
  • id: 14872722
    {'degree': 12, 'field': [321807721, 0, -63926616, 0, 7137780, 0, -350794, 0, 10140, 0, -156, 0, 1], 'lmfdb_label': '356928.dx2', 'torsion': [3, 3]}
  • id: 14872725
    {'degree': 18, 'field': [40281538268, -65238484512, 68205079062, -43861799272, 13418437467, -728869788, -468233438, 57565134, -655371, 4881488, -953001, -219534, 69225, -624, -339, -114, -18, 0, 1], 'lmfdb_label': '356928.dx2', 'torsion': [6]}
  • id: 14872724
    {'degree': 18, 'field': [16360607322450, 3145265192880, -2464447873428, -176121505980, 880165641690, -325662485148, 91178610849, -1620705348, -13127292, -521478576, 141176259, 2960172, -2803022, 9780, 35379, -164, -258, 0, 1], 'lmfdb_label': '356928.dx2', 'torsion': [9]}
• 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: 8834997
    {'conductor': 356928, 'conductor_valuation': 6, 'discriminant_valuation': 57, 'j_denominator_valuation': 39, 'kodaira_symbol': -51, 'lmfdb_label': '356928.dx2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 8834998
    {'conductor': 356928, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '356928.dx2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8834999
    {'conductor': 356928, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '356928.dx2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 8835000
    {'conductor': 356928, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '356928.dx2', 'prime': 13, 'reduction_type': 0, '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: 3890215
    {'adelic_gens': [[4, 3, 9, 7], [146, 3291, 439, 1723], [1715, 3426, 1713, 3413], [937, 6, 2811, 19], [2575, 6, 0, 1], [791, 3426, 2373, 3413], [3427, 6, 3426, 7], [1, 6, 0, 1], [3, 4, 8, 11], [1, 0, 6, 1]], 'adelic_image': '3432.16.0.?', 'conductor': 356928, 'lmfdb_label': '356928.dx2', 'prime': 0}
  • id: 1232058
    {'conductor': 356928, 'elladic_image': '3.4.0.1', 'lmfdb_label': '356928.dx2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 356928.dx does not appear in ec_padic