Elliptic curve data - 52416.dr2

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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': '52416gi', 'Clabel': '52416gi2', 'Cnumber': 2, 'abc_quality': 0.946715860731643, 'absD': 130854932103168, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, 0, 0, -2460, 552368], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 52416, 'degree': 98304, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3884215731124978973494895597', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 95, 'isogeny_degrees': [1, 2], 'jinv': [-137842000, 10955763], 'lmfdb_iso': '52416.dr', 'lmfdb_label': '52416.dr2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -68, 2580], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '52.6.0.c.1', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.80112071961063420652216940908', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 6, 5824], [7, 8, 7488], [13, 14, 4032]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.030443718125173523998429466205', 'prec': 107}, 'szpiro_ratio': 3.677850909295056, '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, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, 0, 1, -2, 1, 2, 0, 0, -6, -4, 2, 0, 12, 2, 6, 6, 14, -12, -10, -10, 0, 2, 4, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 52416, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '52416.dr', 'trace_hash': 349284221987505782}
• 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': '0.062234663328492554340812035017', 'prec': 107}, 'conductor': 52416, 'gens': [[-8, 756, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.80112071961063420652216940908', 'prec': 103}], 'lmfdb_label': '52416.dr2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.48207126554893141716946956720', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.1791564665627051412816665994670113008', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-92, 0, 1]], 'xcoord_integral_points': [-92, -8, 116, 181]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 1, 0], '7': [2, 0], '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '52416.dr2'}
• ec_torsion_growth •

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

  
  
  • id: 2539939
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '52416.dr2', 'torsion': [2, 2]}
  • id: 2539940
    {'degree': 4, 'field': [-12, 0, 2, 0, 1], 'lmfdb_label': '52416.dr2', 'torsion': [4]}
  • id: 2539943
    {'degree': 8, 'field': [-507, 0, -378, 0, -90, 0, 4, 0, 1], 'lmfdb_label': '52416.dr2', 'torsion': [6]}
  • id: 2539941
    {'degree': 8, 'field': [49, 0, 4, 0, -9, 0, -2, 0, 1], 'lmfdb_label': '52416.dr2', 'torsion': [2, 4]}
  • id: 2539942
    {'degree': 8, 'field': [144, 0, 24, 0, 16, 0, -2, 0, 1], 'lmfdb_label': '52416.dr2', 'torsion': [2, 4]}
  • id: 2539945
    {'degree': 16, 'field': [461041, 0, 371768, 0, 193252, 0, 52052, 0, 6646, 0, -304, 0, -152, 0, -4, 0, 1], 'lmfdb_label': '52416.dr2', 'torsion': [2, 6]}
  • id: 2539944
    {'degree': 16, 'field': [2008176, -273120, -1228800, 2354784, 369964, -1645504, 194968, 304916, -76975, -1732, 2080, -332, -430, 196, -8, -8, 1], 'lmfdb_label': '52416.dr2', '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: 1256668
    {'conductor': 52416, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '52416.dr2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1256669
    {'conductor': 52416, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '52416.dr2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1256670
    {'conductor': 52416, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '52416.dr2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1256671
    {'conductor': 52416, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '52416.dr2', '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: 2012377
    {'adelic_gens': [[1, 2, 2, 5], [145, 4, 134, 9], [106, 1, 103, 0], [3, 4, 8, 11], [153, 4, 152, 5], [1, 4, 0, 1], [41, 118, 116, 39], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 52416, 'lmfdb_label': '52416.dr2', 'prime': 0}
  • id: 224228
    {'conductor': 52416, 'elladic_image': '2.3.0.1', 'lmfdb_label': '52416.dr2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2641297
    {'lmfdb_iso': '52416.dr', 'p': 11, 'prec': 20, 'unit': 4981099328255892366, 'val': 1}
  • id: 2641304
    {'lmfdb_iso': '52416.dr', 'p': 17, 'prec': 20, 'unit': 181408380025845466946709, 'val': 1}
  • id: 2641302
    {'lmfdb_iso': '52416.dr', 'p': 29, 'prec': 20, 'unit': 4484640326047016593420850814, 'val': 1}
  • id: 2641310
    {'lmfdb_iso': '52416.dr', 'p': 31, 'prec': 20, 'unit': 17755153946872043181563191412, 'val': 1}
  • id: 2641298
    {'lmfdb_iso': '52416.dr', 'p': 37, 'prec': 20, 'unit': 615512562224973178137257251684, 'val': 1}
  • id: 2641301
    {'lmfdb_iso': '52416.dr', 'p': 43, 'prec': 20, 'unit': 9131969083406641314777476540908, 'val': 1}
  • id: 2641303
    {'lmfdb_iso': '52416.dr', 'p': 47, 'prec': 20, 'unit': 12229694443989706013058872353256, 'val': 1}
  • id: 2641306
    {'lmfdb_iso': '52416.dr', 'p': 53, 'prec': 20, 'unit': 28898478973795325192299372424053, 'val': 1}
  • id: 2641308
    {'lmfdb_iso': '52416.dr', 'p': 59, 'prec': 20, 'unit': 2213275472305924780432366774586865, 'val': 1}
  • id: 2641309
    {'lmfdb_iso': '52416.dr', 'p': 61, 'prec': 20, 'unit': 408477621995061798319365817405802, 'val': 1}
  • id: 2641296
    {'lmfdb_iso': '52416.dr', 'p': 67, 'prec': 20, 'unit': 37140431130973899610485570320091477, 'val': 1}
  • id: 2641299
    {'lmfdb_iso': '52416.dr', 'p': 71, 'prec': 20, 'unit': 73524133086652844105849229844801940, 'val': 1}
  • id: 2641300
    {'lmfdb_iso': '52416.dr', 'p': 73, 'prec': 20, 'unit': 190900577729061072602667884836546146, 'val': 1}
  • id: 2641305
    {'lmfdb_iso': '52416.dr', 'p': 83, 'prec': 20, 'unit': 104467879601644923171523517479169567, 'val': 1}
  • id: 2641307
    {'lmfdb_iso': '52416.dr', 'p': 89, 'prec': 20, 'unit': 15770091540255977121874261504630026, 'val': 2}
  • id: 2641295
    {'lmfdb_iso': '52416.dr', 'p': 97, 'prec': 20, 'unit': 53442970957762838335991483282752635703, 'val': 1}