Elliptic curve data - 7616.j1

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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': '7616k', 'Clabel': '7616k2', 'Cnumber': 2, 'abc_quality': 0.962208541820214, 'absD': 363797676032, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 136, 'ainvs': [0, -1, 0, -1793, -2911], 'analytic_rank': 1, 'bad_primes': [2, 7, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 7616, 'degree': 6144, 'elladic_images': ['8.6.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.90811738381421587019299164634', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2], 'jinv': [2433138625, 1387778], 'lmfdb_iso': '7616.j', 'lmfdb_label': '7616.j1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -28, -5], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.b.1', '68.6.0.c.1', '136.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.93092807578832354592337192131', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.13160338702570209393285653585', 'prec': 107}, 'szpiro_ratio': 3.813948539255326, '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, 2, 0, 0, 0, 1, 0, 1, 0, -2, 0, 2, 0, 0, 0, -1, 0, 0, 0], 'aplist': [0, 2, 0, 1, -2, 2, -1, 0, -4, -4, 0, -8, -2, 0, 0, -2, 4, 12, -8, -12, -14, -12, 4, -6, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 7616, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '7616.j', 'trace_hash': 2120689163947663472}
• 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': '0.16263696549665591890082700088', 'prec': 103}, 'conductor': 7616, 'gens': [[85, 672, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.93092807578832354592337192131', 'prec': 103}], 'lmfdb_label': '7616.j1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.79384153924821531664321655706', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.9120750129054560722368461754117626787', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-41, 0, 1]], 'xcoord_integral_points': [-41, 85]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [3, 5, 0], '7': [4, 0], '11': [3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [3, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '7616.j1'}
• ec_torsion_growth •

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

  
  
  • id: 399688
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '7616.j1', 'torsion': [2, 2]}
  • id: 399689
    {'degree': 4, 'field': [4, -2, 0, -1, 1], 'lmfdb_label': '7616.j1', 'torsion': [4]}
  • id: 399692
    {'degree': 8, 'field': [-12, 0, -62, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '7616.j1', 'torsion': [6]}
  • id: 399691
    {'degree': 8, 'field': [1, 0, -12, 0, -8, 0, 4, 0, 1], 'lmfdb_label': '7616.j1', 'torsion': [2, 4]}
  • id: 399690
    {'degree': 8, 'field': [8, -8, 9, -2, 3, 20, 3, -2, 1], 'lmfdb_label': '7616.j1', 'torsion': [2, 4]}
  • id: 399694
    {'degree': 16, 'field': [28224, 0, -54720, 0, 20100, 0, -1232, 0, -352, 0, -668, 0, 88, 0, -16, 0, 1], 'lmfdb_label': '7616.j1', 'torsion': [2, 6]}
  • id: 399693
    {'degree': 16, 'field': [329816, 464064, 530392, 167248, 24978, -74152, 9132, 9112, 12963, -2332, -652, -420, 110, 68, -12, -4, 1], 'lmfdb_label': '7616.j1', '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: 157263
    {'conductor': 7616, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '7616.j1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 157264
    {'conductor': 7616, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '7616.j1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 157265
    {'conductor': 7616, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '7616.j1', 'prime': 17, '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: 1714350
    {'adelic_gens': [[133, 4, 132, 5], [2, 1, 67, 0], [1, 4, 0, 1], [1, 0, 4, 1], [3, 4, 8, 11], [121, 18, 16, 119], [1, 2, 2, 5], [105, 4, 74, 9]], 'adelic_image': '136.12.0.?', 'conductor': 7616, 'lmfdb_label': '7616.j1', 'prime': 0}
  • id: 37455
    {'conductor': 7616, 'elladic_image': '8.6.0.6', 'lmfdb_label': '7616.j1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 310509
    {'lmfdb_iso': '7616.j', 'p': 11, 'prec': 20, 'unit': 8620708666395618, 'val': 2}
  • id: 310511
    {'lmfdb_iso': '7616.j', 'p': 13, 'prec': 20, 'unit': 472603512852220867717, 'val': 1}
  • id: 310516
    {'lmfdb_iso': '7616.j', 'p': 23, 'prec': 20, 'unit': 796482861102085142250333, 'val': 2}
  • id: 310510
    {'lmfdb_iso': '7616.j', 'p': 29, 'prec': 20, 'unit': 1229847466531102805489486451, 'val': 1}
  • id: 310506
    {'lmfdb_iso': '7616.j', 'p': 37, 'prec': 20, 'unit': 455887279201874048819673651843, 'val': 1}
  • id: 310508
    {'lmfdb_iso': '7616.j', 'p': 41, 'prec': 20, 'unit': 654247781806412887064527383188, 'val': 1}
  • id: 310514
    {'lmfdb_iso': '7616.j', 'p': 53, 'prec': 20, 'unit': 167529687955509466206344911580071, 'val': 1}
  • id: 310518
    {'lmfdb_iso': '7616.j', 'p': 59, 'prec': 20, 'unit': 3015524342474888631312306280444423, 'val': 1}
  • id: 310519
    {'lmfdb_iso': '7616.j', 'p': 61, 'prec': 20, 'unit': 3438688039142658332941333798385578, 'val': 1}
  • id: 310505
    {'lmfdb_iso': '7616.j', 'p': 67, 'prec': 20, 'unit': 17831756298159990642295429695027070, 'val': 1}
  • id: 310507
    {'lmfdb_iso': '7616.j', 'p': 71, 'prec': 20, 'unit': 56710138112875494968723246881930843, 'val': 1}
  • id: 310515
    {'lmfdb_iso': '7616.j', 'p': 73, 'prec': 20, 'unit': 77045284239372086380642917616113390, 'val': 1}
  • id: 310512
    {'lmfdb_iso': '7616.j', 'p': 79, 'prec': 20, 'unit': 640333219871376130000548411868784781, 'val': 1}
  • id: 310513
    {'lmfdb_iso': '7616.j', 'p': 83, 'prec': 20, 'unit': 1211181286245447495416475024009241062, 'val': 1}
  • id: 310517
    {'lmfdb_iso': '7616.j', 'p': 89, 'prec': 20, 'unit': 3727531365260488427859967369178381941, 'val': 1}
  • id: 310504
    {'lmfdb_iso': '7616.j', 'p': 97, 'prec': 20, 'unit': 51905285217179426407312797816507650198, 'val': 1}