Elliptic curve data - 296.a1

Formats: - HTML - YAML - JSON - 2025-03-07T06:06:35.824995

• 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': '296a', 'Clabel': '296a1', 'Cnumber': 1, 'abc_quality': 0.7452705255457956, 'absD': 9472, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 74, 'ainvs': [0, -1, 0, -9, 13], 'analytic_rank': 1, 'bad_primes': [2, 37], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 296, 'degree': 16, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.50223979968578597679438261871', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [351232, 37], 'lmfdb_iso': '296.a', 'lmfdb_label': '296.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -9, 13], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['74.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 10, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.085352993466792815626652379363', 'prec': 107}, 'semistable': False, 'serre_invariants': [[2, 2, 37], [37, 38, 8]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.96433792005908284973920403302', 'prec': 107}, 'szpiro_ratio': 3.218492582806522, '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, -2, 0, 1, 0, -2, 0, 1, 0, -6, 0, 2, 0, -4, 0, -8, 0], 'aplist': [0, -1, -2, 1, 1, -6, -4, -8, 6, 2, -4, -1, 7, 2, 9, -3, -12, 4, 0, 7, 7, 0, 3, -12, -8], 'class_deg': 1, 'class_size': 1, 'conductor': 296, 'isogeny_matrix': [[1]], 'lmfdb_iso': '296.a', 'trace_hash': 1525476278298929105}
• 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': '2.7304859564233922018195193783', 'prec': 100}, 'conductor': 296, 'gens': [[1, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.085352993466792815626652379363', 'prec': 107}], 'lmfdb_label': '296.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '3.9715557927573364071121353165', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3559367025288803838977031862744230847', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-3, 1, 3, 4, 43]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [5, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '296.a1'}
• ec_torsion_growth •

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

  
  
  • id: 12482
    {'degree': 3, 'field': [1, -3, -1, 1], 'lmfdb_label': '296.a1', 'torsion': [2]}
  • id: 12483
    {'degree': 6, 'field': [1, -5, 0, 9, -2, -3, 1], 'lmfdb_label': '296.a1', 'torsion': [2, 2]}
  • id: 12484
    {'degree': 8, 'field': [-147, 0, 232, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '296.a1', 'torsion': [3]}
  • id: 12485
    {'degree': 12, 'field': [1, 6, -20, -6, -21, 24, 16, -28, 31, -38, 20, -6, 1], 'lmfdb_label': '296.a1', 'torsion': [4]}
• 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: 2719
    {'conductor': 296, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '296.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2720
    {'conductor': 296, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '296.a1', 'prime': 37, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  {'adelic_gens': [[39, 2, 39, 3], [73, 2, 72, 3], [1, 2, 0, 1], [1, 0, 2, 1], [1, 1, 73, 0]], 'adelic_image': '74.2.0.?', 'conductor': 296, 'lmfdb_label': '296.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 3021
    {'lmfdb_iso': '296.a', 'p': 5, 'prec': 20, 'unit': 12691698654338, 'val': 1}
  • id: 3022
    {'lmfdb_iso': '296.a', 'p': 7, 'prec': 20, 'unit': 57289970224341821, 'val': -1}
  • id: 3020
    {'lmfdb_iso': '296.a', 'p': 11, 'prec': 20, 'unit': 301177503916926368111, 'val': -1}
  • id: 3026
    {'lmfdb_iso': '296.a', 'p': 13, 'prec': 20, 'unit': 375686495986376082555, 'val': 1}
  • id: 3028
    {'lmfdb_iso': '296.a', 'p': 17, 'prec': 20, 'unit': 209733825178205564205645, 'val': 1}
  • id: 3029
    {'lmfdb_iso': '296.a', 'p': 19, 'prec': 20, 'unit': 807898913902570498524482, 'val': 1}
  • id: 3032
    {'lmfdb_iso': '296.a', 'p': 23, 'prec': 20, 'unit': 20777089777065356329556177, 'val': 1}
  • id: 3025
    {'lmfdb_iso': '296.a', 'p': 29, 'prec': 20, 'unit': 3171858819247089887757148536, 'val': 1}
  • id: 3037
    {'lmfdb_iso': '296.a', 'p': 31, 'prec': 20, 'unit': 10337324446849781508224025333, 'val': 1}
  • id: 3023
    {'lmfdb_iso': '296.a', 'p': 41, 'prec': 20, 'unit': 90015363289366811957044152440, 'val': 2}
  • id: 3024
    {'lmfdb_iso': '296.a', 'p': 43, 'prec': 20, 'unit': 7721000191993516957898746020872, 'val': 1}
  • id: 3027
    {'lmfdb_iso': '296.a', 'p': 47, 'prec': 20, 'unit': 42489094543040367840750921757197, 'val': 1}
  • id: 3030
    {'lmfdb_iso': '296.a', 'p': 53, 'prec': 20, 'unit': 52394482095289225703172477636092, 'val': 1}
  • id: 3035
    {'lmfdb_iso': '296.a', 'p': 59, 'prec': 20, 'unit': 4011308632093525179570325226847028, 'val': 1}
  • id: 3036
    {'lmfdb_iso': '296.a', 'p': 61, 'prec': 20, 'unit': 3762075838057749573837649731674987, 'val': 1}
  • id: 3034
    {'lmfdb_iso': '296.a', 'p': 71, 'prec': 20, 'unit': 290962473272308442522982367495926, 'val': 2}
  • id: 3031
    {'lmfdb_iso': '296.a', 'p': 73, 'prec': 20, 'unit': 172401511827738248222525094072098175, 'val': 1}
  • id: 3019
    {'lmfdb_iso': '296.a', 'p': 83, 'prec': 20, 'unit': 2604744802469212852789205251113788222, 'val': 1}
  • id: 3033
    {'lmfdb_iso': '296.a', 'p': 89, 'prec': 20, 'unit': 6135501376854333122852129026205538987, 'val': 1}
  • id: 3018
    {'lmfdb_iso': '296.a', 'p': 97, 'prec': 20, 'unit': 35292644766982958358505472932221892355, 'val': 1}