Elliptic curve data - 1296.f3

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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': '1296k', 'Clabel': '1296k2', 'Cnumber': 2, 'abc_quality': 1.1780968639246816, 'absD': 1934917632, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 504, 'ainvs': [0, 0, 0, -675, 7074], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 1296, 'degree': 432, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.53886632924398368439301861892', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 5, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-140625, 8], 'lmfdb_iso': '1296.f', 'lmfdb_label': '1296.f3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -42, -100], 'min_quad_twist_disc': -4, 'modell_images': ['3B', '7B'], 'modm_images': ['3.4.0.a.1', '7.8.0.a.1', '8.2.0.a.1', '12.8.0-3.a.1.2', '21.64.1.a.3', '24.16.0-24.a.1.7', '56.16.0.a.1', '63.192.5.e.4', '84.128.1.?', '168.256.5.?', '252.384.5.?', '504.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 2, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.14667492704785354440879951359', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 81], [3, 4, 8]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0697910918727197011869178666', 'prec': 103}, 'szpiro_ratio': 4.360449716306379, '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, -2, 0, 0, 0, -3, 0, 2, 0, 0, 0, 3, 0, 1, 0], 'aplist': [0, 0, 0, -2, -3, 2, 3, 1, -6, -6, 4, -4, -9, 1, -6, -12, 3, 8, -5, -12, 11, 4, 12, -6, 5], 'class_deg': 21, 'class_size': 4, 'conductor': 1296, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '1296.f', 'trace_hash': 65372923418112730}
• 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': '0.34036637824034343829847929677', 'prec': 103}, 'conductor': 1296, 'gens': [[33, 144, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.14667492704785354440879951359', 'prec': 103}], 'lmfdb_label': '1296.f3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.4583600522209898882505817355', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5668582512282109269984226132308924416', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': [-30, 1, 15, 33]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 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': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1296.f3'}
• ec_torsion_growth •

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

  
  
  • id: 64294
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1296.f3', 'torsion': [3]}
  • id: 64295
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '1296.f3', 'torsion': [2]}
  • id: 64299
    {'degree': 6, 'field': [-12, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '1296.f3', 'torsion': [6]}
  • id: 64298
    {'degree': 6, 'field': [-3, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '1296.f3', 'torsion': [21]}
  • id: 64296
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '1296.f3', 'torsion': [2, 2]}
  • id: 64297
    {'degree': 6, 'field': [9, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1296.f3', 'torsion': [3]}
  • id: 64300
    {'degree': 12, 'field': [-8, 48, -102, 70, 90, -252, 282, -198, 90, -20, 3, -3, 1], 'lmfdb_label': '1296.f3', 'torsion': [4]}
  • id: 64301
    {'degree': 12, 'field': [4, 12, 66, -170, 135, -108, 135, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '1296.f3', 'torsion': [3, 3]}
  • id: 64302
    {'degree': 12, 'field': [262, -108, 198, -268, 225, -180, 102, -36, 36, -16, 0, 0, 1], 'lmfdb_label': '1296.f3', 'torsion': [2, 6]}
  • id: 64303
    {'degree': 18, 'field': [-48, 0, 432, 0, -1260, 0, 2073, 0, -2106, 0, 1359, 0, -552, 0, 135, 0, -18, 0, 1], 'lmfdb_label': '1296.f3', 'torsion': [9]}
  • id: 64305
    {'degree': 18, 'field': [-27, 0, 0, 0, 54, 0, 27, 0, -27, 0, -9, 0, -15, 0, 0, 0, -3, 0, 1], 'lmfdb_label': '1296.f3', 'torsion': [42]}
  • id: 64304
    {'degree': 18, 'field': [64, 0, 0, 0, 0, 0, -87, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1296.f3', '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: 19369
    {'conductor': 1296, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '1296.f3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 19370
    {'conductor': 1296, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '1296.f3', 'prime': 3, '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

  
  
  • id: 1672693
    {'adelic_gens': [[281, 392, 112, 393], [327, 494, 56, 87], [1, 426, 42, 253], [1, 216, 0, 1], [1, 0, 462, 1], [209, 462, 273, 293], [85, 42, 189, 43], [337, 168, 336, 169], [1, 0, 168, 1], [22, 321, 189, 169], [1, 42, 0, 73], [1, 0, 420, 1], [1, 168, 0, 1], [463, 282, 420, 295]], 'adelic_image': '504.768.21.?', 'conductor': 1296, 'lmfdb_label': '1296.f3', 'prime': 0}
  • id: 6209
    {'conductor': 1296, 'elladic_image': '8.2.0.1', 'lmfdb_label': '1296.f3', 'modell_image': '2G', 'prime': 2}
  • id: 6210
    {'conductor': 1296, 'elladic_image': '3.4.0.1', 'lmfdb_label': '1296.f3', 'modell_image': '3B', 'prime': 3}
  • id: 6211
    {'conductor': 1296, 'elladic_image': '7.8.0.1', 'lmfdb_label': '1296.f3', 'modell_image': '7B', 'prime': 7}
• ec_padic •

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

  
  
  • id: 32670
    {'lmfdb_iso': '1296.f', 'p': 7, 'prec': 20, 'unit': 8644113572719825, 'val': 1}
  • id: 32671
    {'lmfdb_iso': '1296.f', 'p': 11, 'prec': 20, 'unit': 5219998873499498175, 'val': 1}
  • id: 32672
    {'lmfdb_iso': '1296.f', 'p': 13, 'prec': 20, 'unit': 1121462870103730270029, 'val': 1}
  • id: 32673
    {'lmfdb_iso': '1296.f', 'p': 17, 'prec': 20, 'unit': 51951256976640022423999, 'val': 1}
  • id: 32674
    {'lmfdb_iso': '1296.f', 'p': 19, 'prec': 20, 'unit': 739614666918034740851060, 'val': -1}
  • id: 32675
    {'lmfdb_iso': '1296.f', 'p': 23, 'prec': 20, 'unit': 46853994078611620013285263, 'val': 1}
  • id: 32676
    {'lmfdb_iso': '1296.f', 'p': 29, 'prec': 20, 'unit': 5307009513857858371688928255, 'val': 1}
  • id: 32677
    {'lmfdb_iso': '1296.f', 'p': 31, 'prec': 20, 'unit': 11793563817323981974237575588, 'val': 1}
  • id: 32678
    {'lmfdb_iso': '1296.f', 'p': 37, 'prec': 20, 'unit': 110393379618094142671394753019, 'val': 1}
  • id: 32679
    {'lmfdb_iso': '1296.f', 'p': 41, 'prec': 20, 'unit': 2446716218273862965568583525295, 'val': 1}
  • id: 32680
    {'lmfdb_iso': '1296.f', 'p': 43, 'prec': 20, 'unit': 334774010748208831573171729181070, 'val': -1}
  • id: 32681
    {'lmfdb_iso': '1296.f', 'p': 47, 'prec': 20, 'unit': 36648392936129685751036015604960, 'val': 1}
  • id: 32682
    {'lmfdb_iso': '1296.f', 'p': 53, 'prec': 20, 'unit': 461241636505318504987764903805955, 'val': 1}
  • id: 32683
    {'lmfdb_iso': '1296.f', 'p': 59, 'prec': 20, 'unit': 2112289741688272556203020699658842, 'val': 1}
  • id: 32684
    {'lmfdb_iso': '1296.f', 'p': 61, 'prec': 20, 'unit': 2121742423040880434333082796332989, 'val': 1}
  • id: 32685
    {'lmfdb_iso': '1296.f', 'p': 67, 'prec': 20, 'unit': 40003079605630550803550940838793208, 'val': 1}
  • id: 32686
    {'lmfdb_iso': '1296.f', 'p': 71, 'prec': 20, 'unit': 130486403268928805859874275876763093, 'val': 1}
  • id: 32687
    {'lmfdb_iso': '1296.f', 'p': 73, 'prec': 20, 'unit': 57881012509226106659868212643869955, 'val': 1}
  • id: 32688
    {'lmfdb_iso': '1296.f', 'p': 79, 'prec': 20, 'unit': 535775712081229870363540138255847834, 'val': 1}
  • id: 32689
    {'lmfdb_iso': '1296.f', 'p': 83, 'prec': 20, 'unit': 130770569148174978002891667334009073, 'val': 1}
  • id: 32690
    {'lmfdb_iso': '1296.f', 'p': 89, 'prec': 20, 'unit': 2279096397194943629578124803245491256, 'val': 1}
  • id: 32691
    {'lmfdb_iso': '1296.f', 'p': 97, 'prec': 20, 'unit': 10622691525937039171435236004023368025, 'val': 1}