Elliptic curve data - 4225.k2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '4225k', 'Clabel': '4225k1', 'Cnumber': 1, 'abc_quality': 0.7910122173261119, 'absD': 4291015625, 'adelic_genus': 41, 'adelic_index': 1152, 'adelic_level': 3120, 'ainvs': [1, 0, 1, -576, -4327], 'analytic_rank': 1, 'bad_primes': [5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4225, 'degree': 1920, 'elladic_images': ['16.24.0.21', '3.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.56394858740738547709120453087', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [4913, 1], 'lmfdb_iso': '4225.k', 'lmfdb_label': '4225.k2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -23, -44], 'min_quad_twist_disc': 5, 'modell_images': ['2B', '3Nn'], 'modm_images': ['2.3.0.a.1', '3.3.0.a.1', '4.6.0.d.1', '6.9.0.a.1', '8.12.0.w.1', '12.18.0.k.1', '16.24.0.o.2', '24.72.2.hl.1', '30.18.0.c.1', '39.6.0.b.1', '40.24.0.el.1', '48.144.5.eo.2', '60.36.0.bz.1', '78.18.0.?', '80.48.1.?', '104.24.0.?', '120.144.5.?', '130.6.0.?', '156.36.1.?', '208.48.1.?', '240.288.13.?', '260.24.0.?', '312.144.7.?', '390.36.1.?', '520.96.1.?', '624.288.17.?', '780.144.3.?', '1040.192.5.?', '1560.576.17.?', '3120.1152.41.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.9467563320990198057247590334', 'prec': 100}, 'semistable': False, 'serre_invariants': [[5, 14, 169], [13, 50, 25]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2843671862835739878727368294', 'prec': 103}, 'szpiro_ratio': 3.6747224601932023, '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, 1, -2, -1, 0, -2, 0, -3, 1, 0, -2, 2, 0, 0, 0, -1, 0, 1, 6, 0], 'aplist': [1, -2, 0, 0, -2, 0, 0, 6, 6, -6, 6, 6, -8, -6, -8, 12, 2, 6, -12, -2, 6, 0, -4, -8, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 4225, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4225.k', 'trace_hash': 105617722066375292}
• 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': '0.32371325359654440599885321758', 'prec': 103}, 'conductor': 4225, 'gens': [[-9, 16, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9467563320990198057247590334', 'prec': 100}], 'lmfdb_label': '4225.k2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.98865501272136107439891233280', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9133254189981077249317963548941769895', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[27, -14, 1]], 'xcoord_integral_points': [-9, 27]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'o?', '3': [3, 0], '5': 'a', '7': [1, 1, 0], '11': [1, 0], '13': 'a', '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4225.k2'}
• ec_torsion_growth •

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

  
  
  • id: 220652
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '4225.k2', 'torsion': [2, 2]}
  • id: 220653
    {'degree': 4, 'field': [-49, 69, -24, -1, 1], 'lmfdb_label': '4225.k2', 'torsion': [2, 4]}
  • id: 220655
    {'degree': 8, 'field': [-39, 78, -247, 221, -95, 6, 8, -2, 1], 'lmfdb_label': '4225.k2', 'torsion': [6]}
  • id: 220654
    {'degree': 8, 'field': [1, 0, 1137, 0, 384, 0, 33, 0, 1], 'lmfdb_label': '4225.k2', 'torsion': [2, 4]}
  • id: 220657
    {'degree': 16, 'field': [-3184, 6568, 5772, -22784, 11118, 16124, -20321, 4418, 5768, -4494, 781, 512, -327, 62, 8, -6, 1], 'lmfdb_label': '4225.k2', 'torsion': [2, 8]}
  • id: 220658
    {'degree': 16, 'field': [81, 297, 2802, 1926, 15883, 34060, 35141, 22733, 8883, 1806, 9, -312, -72, -43, 8, -2, 1], 'lmfdb_label': '4225.k2', 'torsion': [3, 6]}
  • id: 220656
    {'degree': 16, 'field': [2401, 0, 22929, 0, 80190, 0, 116671, 0, 53794, 0, 10271, 0, 990, 0, 49, 0, 1], 'lmfdb_label': '4225.k2', 'torsion': [4, 4]}
  • id: 220659
    {'degree': 16, 'field': [2601, 0, 4290, 0, 9013, 0, 1755, 0, 864, 0, -195, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '4225.k2', 'torsion': [2, 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: 79661
    {'conductor': 4225, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4225.k2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 79662
    {'conductor': 4225, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '4225.k2', '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: 1691504
    {'adelic_gens': [[3073, 48, 3072, 49], [1, 24, 24, 577], [1, 0, 48, 1], [272, 31, 1681, 2656], [33, 16, 2000, 2577], [1, 48, 0, 1], [2081, 48, 2364, 2453], [19, 18, 210, 199], [608, 3099, 1821, 752], [1441, 48, 2010, 1231], [2081, 48, 0, 1]], 'adelic_image': '3120.1152.41.?', 'conductor': 4225, 'lmfdb_label': '4225.k2', 'prime': 0}
  • id: 21029
    {'conductor': 4225, 'elladic_image': '16.24.0.21', 'lmfdb_label': '4225.k2', 'modell_image': '2B', 'prime': 2}
  • id: 21030
    {'conductor': 4225, 'elladic_image': '3.3.0.1', 'lmfdb_label': '4225.k2', 'modell_image': '3Nn', 'prime': 3}
• ec_padic •

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

  
  
  • id: 149818
    {'lmfdb_iso': '4225.k', 'p': 11, 'prec': 20, 'unit': 7966055727338546096, 'val': 1}
  • id: 149819
    {'lmfdb_iso': '4225.k', 'p': 19, 'prec': 20, 'unit': 325814300292250399454911, 'val': 1}
  • id: 149822
    {'lmfdb_iso': '4225.k', 'p': 23, 'prec': 20, 'unit': 20306698716103338643066709, 'val': 1}
  • id: 149816
    {'lmfdb_iso': '4225.k', 'p': 29, 'prec': 20, 'unit': 77298407523638595188312982, 'val': 1}
  • id: 149826
    {'lmfdb_iso': '4225.k', 'p': 31, 'prec': 20, 'unit': 14353207632001565149745075977, 'val': 1}
  • id: 149812
    {'lmfdb_iso': '4225.k', 'p': 37, 'prec': 20, 'unit': 214399893544780625211739629595, 'val': 1}
  • id: 149814
    {'lmfdb_iso': '4225.k', 'p': 41, 'prec': 20, 'unit': 3958957232111893172027327213675, 'val': 1}
  • id: 149815
    {'lmfdb_iso': '4225.k', 'p': 43, 'prec': 20, 'unit': 5599090691513198829179893166277, 'val': 1}
  • id: 149817
    {'lmfdb_iso': '4225.k', 'p': 47, 'prec': 20, 'unit': 18126967659268143350409653051517, 'val': 1}
  • id: 149820
    {'lmfdb_iso': '4225.k', 'p': 53, 'prec': 20, 'unit': 16694029401592796480859726464391, 'val': 1}
  • id: 149824
    {'lmfdb_iso': '4225.k', 'p': 59, 'prec': 20, 'unit': 897628649932252594926386027144210, 'val': 1}
  • id: 149825
    {'lmfdb_iso': '4225.k', 'p': 61, 'prec': 20, 'unit': 5127418308415540576499761583406235, 'val': 1}
  • id: 149811
    {'lmfdb_iso': '4225.k', 'p': 67, 'prec': 20, 'unit': 19617708013876278218078918879690956, 'val': 1}
  • id: 149813
    {'lmfdb_iso': '4225.k', 'p': 71, 'prec': 20, 'unit': 147423439681870011678734592769351650, 'val': 1}
  • id: 149821
    {'lmfdb_iso': '4225.k', 'p': 73, 'prec': 20, 'unit': 5067941760067869951905015681111896, 'val': 1}
  • id: 149810
    {'lmfdb_iso': '4225.k', 'p': 83, 'prec': 20, 'unit': 2884189835684986883520285355099843648, 'val': 1}
  • id: 149823
    {'lmfdb_iso': '4225.k', 'p': 89, 'prec': 20, 'unit': 8089605269543403644106044844163659813, 'val': 1}
  • id: 149809
    {'lmfdb_iso': '4225.k', 'p': 97, 'prec': 20, 'unit': 35665501027736468679454873834565154823, 'val': 1}