Elliptic curve data - 28224.dp2

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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': '28224b', 'Clabel': '28224b1', 'Cnumber': 1, 'absD': 4148928, 'ainvs': [0, 0, 0, 0, 98], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 3, 'class_size': 2, 'cm': -3, 'conductor': 28224, 'degree': 3456, 'elladic_images': ['7.84.1.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.051254049629266735730657578080', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 93, 'isogeny_degrees': [1, 3], 'jinv': [0, 1], 'lmfdb_iso': '28224.dp', 'lmfdb_label': '28224.dp2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 12], 'min_quad_twist_disc': 8, 'modell_images': ['7Ns.6.1.2'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.52431451180667969106882694562', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 147], [3, 6, 3136], [7, 20, 576]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 2.2144067157935123, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0], 'aplist': [0, 0, 0, 0, 0, 7, 0, 7, 0, 0, -7, 1, 0, -5, 0, 0, 0, -14, -11, 0, -7, -13, 0, 0, 14], 'class_deg': 3, 'class_size': 2, 'conductor': 28224, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '28224.dp', 'trace_hash': 1605218452106851316}
• 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': '1.1079462754167910484468802622', 'prec': 100}, 'conductor': 28224, 'gens': [[7, 21, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.52431451180667969106882694562', 'prec': 103}], 'lmfdb_label': '28224.dp2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.9590912388546801294919959929', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.1630797989090095649457083062439224863', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [5, 1, 0], '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [3, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '28224.dp2'}
• ec_torsion_growth •

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

  
  
  • id: 1412294
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [3]}
  • id: 1412295
    {'degree': 3, 'field': [1, 5, -1, 1], 'lmfdb_label': '28224.dp2', 'torsion': [2]}
  • id: 1412298
    {'degree': 6, 'field': [-98, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [6]}
  • id: 1412296
    {'degree': 6, 'field': [27, 9, -8, -3, 4, -3, 1], 'lmfdb_label': '28224.dp2', 'torsion': [2, 2]}
  • id: 1412297
    {'degree': 6, 'field': [265, 252, 108, -14, 18, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [3]}
  • id: 1412302
    {'degree': 12, 'field': [-1728, 0, 864, 0, 4608, 0, -792, 0, -108, 0, 12, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [7]}
  • id: 1412299
    {'degree': 12, 'field': [-524, -16, -24, -680, -1136, -120, 808, 264, -54, -16, -2, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [4]}
  • id: 1412303
    {'degree': 12, 'field': [36, 0, 48, 0, 52, 0, 28, 0, 12, 0, -2, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [2, 6]}
  • id: 1412300
    {'degree': 12, 'field': [1681, 3444, 6564, -140, -786, 1176, 350, 0, 24, -28, 6, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [3, 3]}
  • id: 1412301
    {'degree': 12, 'field': [12096, 0, 6048, 0, 3024, 0, 288, 0, 24, 0, -18, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [7]}
  • id: 1412304
    {'degree': 18, 'field': [-12088, -22416, 35820, 37608, 16218, -35820, -7791, -21318, 117, 14330, 819, -1674, -1194, 6, 315, -12, -24, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [9]}
  • id: 1412305
    {'degree': 18, 'field': [384, 0, 768, 0, 5760, 0, 3268, 0, 2472, 0, 888, 0, 332, 0, 60, 0, 12, 0, 1], 'lmfdb_label': '28224.dp2', 'torsion': [6]}
• 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: 653387
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '28224.dp2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 653388
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '28224.dp2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 653389
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '28224.dp2', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  {'conductor': 28224, 'elladic_image': '7.84.1.1', 'lmfdb_label': '28224.dp2', 'modell_image': '7Ns.6.1.2', 'prime': 7}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 1355503
    {'lmfdb_iso': '28224.dp', 'p': 13, 'prec': 20, 'unit': 641019841954677818482, 'val': 1}
  • id: 1355505
    {'lmfdb_iso': '28224.dp', 'p': 19, 'prec': 20, 'unit': 571411064804218406439655, 'val': 1}
  • id: 1355507
    {'lmfdb_iso': '28224.dp', 'p': 31, 'prec': 20, 'unit': 21398528825898847470566132094, 'val': 1}
  • id: 1355500
    {'lmfdb_iso': '28224.dp', 'p': 37, 'prec': 20, 'unit': 12359698730689246657214948357657, 'val': 0}
  • id: 1355502
    {'lmfdb_iso': '28224.dp', 'p': 43, 'prec': 20, 'unit': 6699868562089203997141225107610, 'val': 1}
  • id: 1355506
    {'lmfdb_iso': '28224.dp', 'p': 61, 'prec': 20, 'unit': 1242234023966326737187141404186211, 'val': 1}
  • id: 1355499
    {'lmfdb_iso': '28224.dp', 'p': 67, 'prec': 20, 'unit': 12453759390784803769309366511552654, 'val': 1}
  • id: 1355501
    {'lmfdb_iso': '28224.dp', 'p': 73, 'prec': 20, 'unit': 68928049770522839433995823072743742, 'val': 1}
  • id: 1355504
    {'lmfdb_iso': '28224.dp', 'p': 79, 'prec': 20, 'unit': 57769771668072326376021136185572922, 'val': 1}
  • id: 1355498
    {'lmfdb_iso': '28224.dp', 'p': 97, 'prec': 20, 'unit': 5932458998378865731886582156190321866, 'val': 1}