Elliptic curve data - 663.a6

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '663b', 'Clabel': '663b6', 'Cnumber': 6, 'abc_quality': 0.9885418782056836, 'absD': 7345472585373, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 3536, 'ainvs': [1, 1, 1, 3876, -89910], 'analytic_rank': 1, 'bad_primes': [3, 13, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 663, 'degree': 1024, 'elladic_images': ['8.48.0.178'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1551559452628778738618944154', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [6439735268725823, 7345472585373], 'lmfdb_iso': '663.a', 'lmfdb_label': '663.a6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 3876, -89910], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.48.0-8.ba.2.6', '52.24.0-52.h.1.1', '104.96.0.?', '272.96.0.?', '3536.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.74395301777770823327716607750', 'prec': 103}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1551559452628778738618944154', 'prec': 100}, 'szpiro_ratio': 5.60297438064727, '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, -1, -1, -2, 1, 0, 3, 1, 2, 4, 1, 1, 0, 2, -1, 1, -1, -4, 2], 'aplist': [-1, -1, -2, 0, 4, 1, 1, -4, 0, -2, -8, -2, 2, -4, 8, -10, 4, 14, -4, 0, -14, -8, -4, -6, -6], 'class_deg': 8, 'class_size': 6, 'conductor': 663, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '663.a', 'trace_hash': 1193554490023354343}
• 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': '0.099230297743061531724649849715', 'prec': 107}, 'conductor': 663, 'gens': [[25, 140, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.74395301777770823327716607750', 'prec': 103}], 'lmfdb_label': '663.a6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.40059551251326720618099269335', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1920969617698112754438579084628276344', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[83, -87, 2]], 'xcoord_integral_points': [25, 1249]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 3], '3': [1, 0], '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [2, 0], '17': [2, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '663.a6'}
• ec_torsion_growth •

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

  
  
  • id: 30700
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '663.a6', 'torsion': [4]}
  • id: 30701
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [4]}
  • id: 30699
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [2, 2]}
  • id: 30704
    {'degree': 4, 'field': [-13, 0, 0, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [8]}
  • id: 30705
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [8]}
  • id: 30702
    {'degree': 4, 'field': [9, 0, 7, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [2, 4]}
  • id: 30703
    {'degree': 4, 'field': [13, 0, 0, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [2, 4]}
  • id: 30706
    {'degree': 4, 'field': [169, 0, 0, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [8]}
  • id: 30710
    {'degree': 8, 'field': [-3, 0, -161, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [6]}
  • id: 30708
    {'degree': 8, 'field': [9, 6, 2, -18, 15, -10, 8, -4, 1], 'lmfdb_label': '663.a6', 'torsion': [2, 8]}
  • id: 30709
    {'degree': 8, 'field': [81, 0, 0, 0, 31, 0, 0, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [2, 8]}
  • id: 30707
    {'degree': 8, 'field': [196, 0, -152, 0, 32, 0, 4, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [4, 4]}
  • id: 30713
    {'degree': 16, 'field': [169, 0, 0, 0, 7605, 0, 0, 0, -1378, 0, 0, 0, -585, 0, 0, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [16]}
  • id: 30712
    {'degree': 16, 'field': [289, -1564, 4232, -4676, 2694, -440, 760, -1372, 1255, -584, 232, -172, 126, -76, 32, -8, 1], 'lmfdb_label': '663.a6', 'torsion': [4, 8]}
  • id: 30716
    {'degree': 16, 'field': [28561, 0, 17576, 0, 2704, 0, 349323, 0, 52728, 0, 2301, 0, 169, 0, 26, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [2, 6]}
  • id: 30718
    {'degree': 16, 'field': [28561, 0, 57122, 0, 28561, 0, -5736, 0, -3882, 0, 402, 0, 16, 0, 8, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [12]}
  • id: 30717
    {'degree': 16, 'field': [66963, 587418, -348568, -489418, 267743, -8180, -35258, 42928, -22128, 5346, 858, -656, -194, 112, 4, -8, 1], 'lmfdb_label': '663.a6', 'torsion': [12]}
  • id: 30711
    {'degree': 16, 'field': [1110916, 0, -58960, 0, 147448, 0, -58912, 0, 2176, 0, 56, 0, 28, 0, 8, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [4, 8]}
  • id: 30714
    {'degree': 16, 'field': [2998219536, 0, 0, 0, -51251616, 0, 0, 0, 2224665, 0, 0, 0, -936, 0, 0, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [16]}
  • id: 30715
    {'degree': 16, 'field': [85632148167696, 0, 0, 0, -112599800352, 0, 0, 0, 375968385, 0, 0, 0, -12168, 0, 0, 0, 1], 'lmfdb_label': '663.a6', 'torsion': [16]}
• 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: 8102
    {'conductor': 663, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '663.a6', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8103
    {'conductor': 663, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '663.a6', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 8104
    {'conductor': 663, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '663.a6', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

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

  
  
  • id: 1668914
    {'adelic_gens': [[1, 16, 0, 1], [1368, 1, 3343, 10], [3521, 16, 3520, 17], [15, 2, 3438, 3523], [1, 0, 16, 1], [1873, 16, 840, 129], [5, 4, 3532, 3533], [3102, 885, 521, 1778], [13, 16, 628, 569]], 'adelic_image': '3536.192.1.?', 'conductor': 663, 'lmfdb_label': '663.a6', 'prime': 0}
  • id: 3023
    {'conductor': 663, 'elladic_image': '8.48.0.178', 'lmfdb_label': '663.a6', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 11905
    {'lmfdb_iso': '663.a', 'p': 5, 'prec': 20, 'unit': 3598002072239, 'val': 1}
  • id: 11897
    {'lmfdb_iso': '663.a', 'p': 11, 'prec': 20, 'unit': 54877297030761928352, 'val': 1}
  • id: 11899
    {'lmfdb_iso': '663.a', 'p': 19, 'prec': 20, 'unit': 306514855978172946019320, 'val': 1}
  • id: 11895
    {'lmfdb_iso': '663.a', 'p': 29, 'prec': 20, 'unit': 5134519084856574289506507383, 'val': 1}
  • id: 11892
    {'lmfdb_iso': '663.a', 'p': 31, 'prec': 20, 'unit': 11924407594100432153828459483, 'val': 1}
  • id: 11891
    {'lmfdb_iso': '663.a', 'p': 37, 'prec': 20, 'unit': 601261315706450051615971826712, 'val': 1}
  • id: 11893
    {'lmfdb_iso': '663.a', 'p': 41, 'prec': 20, 'unit': 4353255953351273729039261754458, 'val': 1}
  • id: 11894
    {'lmfdb_iso': '663.a', 'p': 43, 'prec': 20, 'unit': 8866840704901093624744381128136, 'val': 1}
  • id: 11903
    {'lmfdb_iso': '663.a', 'p': 47, 'prec': 20, 'unit': 44527791637825948712306288179322, 'val': 1}
  • id: 11900
    {'lmfdb_iso': '663.a', 'p': 53, 'prec': 20, 'unit': 331628268834065266219428043951867, 'val': 1}
  • id: 11898
    {'lmfdb_iso': '663.a', 'p': 59, 'prec': 20, 'unit': 3136214508843713289837872110139038, 'val': 1}
  • id: 11904
    {'lmfdb_iso': '663.a', 'p': 61, 'prec': 20, 'unit': 3278789035773472306509878279524231, 'val': 1}
  • id: 11890
    {'lmfdb_iso': '663.a', 'p': 67, 'prec': 20, 'unit': 33140489309116980840178606893963601, 'val': 1}
  • id: 11901
    {'lmfdb_iso': '663.a', 'p': 73, 'prec': 20, 'unit': 87744626518980661840850065928228203, 'val': 1}
  • id: 11896
    {'lmfdb_iso': '663.a', 'p': 79, 'prec': 20, 'unit': 840994640339092002658993630704572502, 'val': 1}
  • id: 11889
    {'lmfdb_iso': '663.a', 'p': 83, 'prec': 20, 'unit': 816470224447469930178329567574063974, 'val': 1}
  • id: 11902
    {'lmfdb_iso': '663.a', 'p': 89, 'prec': 20, 'unit': 9611716939372265270412845330663836495, 'val': 1}
  • id: 11888
    {'lmfdb_iso': '663.a', 'p': 97, 'prec': 20, 'unit': 6443883510143381571720050901884658124, 'val': 1}