Elliptic curve data - 11616.s3

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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': '11616m', 'Clabel': '11616m1', 'Cnumber': 1, 'abc_quality': 0.9303769565820871, 'absD': 1111236439104, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 88, 'ainvs': [0, 1, 0, -4154, -91104], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 11616, 'degree': 15360, 'elladic_images': ['8.24.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0375942365750321097791697880', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2], 'jinv': [69934528, 9801], 'lmfdb_iso': '11616.s', 'lmfdb_label': '11616.s3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -34, -56], 'min_quad_twist_disc': 44, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '8.24.0-8.b.1.3', '44.24.0-44.a.1.2', '88.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.2356731687291327613991228924', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 121], [3, 4, 3872], [11, 72, 96]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.50792699010412581696041806171', 'prec': 107}, 'szpiro_ratio': 3.911194673133604, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 6, 0, -2, 0, -2, 0, 4, 0], 'aplist': [0, 1, -2, 0, 0, 6, -2, 4, -4, -2, -4, -2, -10, 4, -4, 6, -12, 6, -4, -4, -10, 16, -4, 10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 11616, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '11616.s', 'trace_hash': 1461893024759404566}
• 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': '0.12553276570767243775551579330', 'prec': 103}, 'conductor': 11616, 'gens': [[121, 1092, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.2356731687291327613991228924', 'prec': 100}], 'lmfdb_label': '11616.s3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.60020767026755079766492094354', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.0845670492353747415628324771623630016', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-26, 0, 1], [73, 0, 1]], 'xcoord_integral_points': [-48, -26, 73, 121]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 5, 0], '11': 'a', '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': '11616.s3'}
• ec_torsion_growth •

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

  
  
  • id: 601076
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '11616.s3', 'torsion': [2, 4]}
  • id: 601078
    {'degree': 4, 'field': [3, -10, 11, -2, 1], 'lmfdb_label': '11616.s3', 'torsion': [2, 4]}
  • id: 601077
    {'degree': 4, 'field': [121, 0, 0, 0, 1], 'lmfdb_label': '11616.s3', 'torsion': [2, 4]}
  • id: 601081
    {'degree': 8, 'field': [-396, -792, 792, -176, 176, -44, 4, -4, 1], 'lmfdb_label': '11616.s3', 'torsion': [2, 6]}
  • id: 601080
    {'degree': 8, 'field': [1, 0, -796, 0, 402, 0, -4, 0, 1], 'lmfdb_label': '11616.s3', 'torsion': [2, 8]}
  • id: 601079
    {'degree': 8, 'field': [81, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '11616.s3', 'torsion': [4, 4]}
  • id: 601083
    {'degree': 16, 'field': [9801, 0, 14256, 0, 5976, 0, 3384, 0, 2806, 0, -112, 0, 24, 0, 8, 0, 1], 'lmfdb_label': '11616.s3', 'torsion': [2, 8]}
  • id: 601082
    {'degree': 16, 'field': [14884, 0, -14256, 0, 13336, 0, -11792, 0, 4824, 0, -440, 0, 4, 0, 0, 0, 1], 'lmfdb_label': '11616.s3', 'torsion': [2, 8]}
  • id: 601084
    {'degree': 16, 'field': [66509, -187816, 260428, -317804, 362336, -333672, 250804, -157940, 82214, -33656, 9564, -1148, -400, 216, -28, -4, 1], 'lmfdb_label': '11616.s3', 'torsion': [2, 12]}
• 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: 249753
    {'conductor': 11616, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '11616.s3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 249754
    {'conductor': 11616, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '11616.s3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 249755
    {'conductor': 11616, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '11616.s3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1741052
    {'adelic_gens': [[31, 86, 0, 87], [69, 2, 42, 87], [85, 4, 84, 5], [1, 4, 0, 1], [45, 4, 2, 9], [1, 0, 4, 1]], 'adelic_image': '88.48.0.?', 'conductor': 11616, 'lmfdb_label': '11616.s3', 'prime': 0}
  • id: 55738
    {'conductor': 11616, 'elladic_image': '8.24.0.6', 'lmfdb_label': '11616.s3', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 503265
    {'lmfdb_iso': '11616.s', 'p': 5, 'prec': 20, 'unit': 12926920930089, 'val': 1}
  • id: 503271
    {'lmfdb_iso': '11616.s', 'p': 13, 'prec': 20, 'unit': 1196295243302846256111, 'val': 1}
  • id: 503273
    {'lmfdb_iso': '11616.s', 'p': 17, 'prec': 20, 'unit': 58805635610568372791229, 'val': 1}
  • id: 503274
    {'lmfdb_iso': '11616.s', 'p': 19, 'prec': 20, 'unit': 35475841623048445440146, 'val': 1}
  • id: 503278
    {'lmfdb_iso': '11616.s', 'p': 23, 'prec': 20, 'unit': 69343913236158119087636771, 'val': 1}
  • id: 503270
    {'lmfdb_iso': '11616.s', 'p': 29, 'prec': 20, 'unit': 1934124925892120237218736868, 'val': 1}
  • id: 503267
    {'lmfdb_iso': '11616.s', 'p': 31, 'prec': 20, 'unit': 9513925677079501154254863195, 'val': 1}
  • id: 503282
    {'lmfdb_iso': '11616.s', 'p': 37, 'prec': 20, 'unit': 14414143074274196017969579726, 'val': 1}
  • id: 503268
    {'lmfdb_iso': '11616.s', 'p': 41, 'prec': 20, 'unit': 718202377840998601778289562687, 'val': 1}
  • id: 503269
    {'lmfdb_iso': '11616.s', 'p': 43, 'prec': 20, 'unit': 288495501746270561503198821150, 'val': 1}
  • id: 503280
    {'lmfdb_iso': '11616.s', 'p': 47, 'prec': 20, 'unit': 39790711747514022820493391868878, 'val': 1}
  • id: 503275
    {'lmfdb_iso': '11616.s', 'p': 53, 'prec': 20, 'unit': 47493690086417413873618006635362, 'val': 1}
  • id: 503276
    {'lmfdb_iso': '11616.s', 'p': 59, 'prec': 20, 'unit': 1363157777474149167943691739469753, 'val': 1}
  • id: 503281
    {'lmfdb_iso': '11616.s', 'p': 61, 'prec': 20, 'unit': 8063032330565118575252235949923610, 'val': 1}
  • id: 503264
    {'lmfdb_iso': '11616.s', 'p': 67, 'prec': 20, 'unit': 34280501761142898549659220280846472, 'val': 1}
  • id: 503266
    {'lmfdb_iso': '11616.s', 'p': 71, 'prec': 20, 'unit': 126681980937002070479311403839370653, 'val': 1}
  • id: 503277
    {'lmfdb_iso': '11616.s', 'p': 73, 'prec': 20, 'unit': 169864359877143214382850632090170880, 'val': 1}
  • id: 503272
    {'lmfdb_iso': '11616.s', 'p': 79, 'prec': 20, 'unit': 963956695026083636615094275727345359, 'val': 1}
  • id: 503263
    {'lmfdb_iso': '11616.s', 'p': 83, 'prec': 20, 'unit': 1885201546211905702509174672298961260, 'val': 1}
  • id: 503279
    {'lmfdb_iso': '11616.s', 'p': 89, 'prec': 20, 'unit': 5594977321301409609072874879746284349, 'val': 1}
  • id: 503262
    {'lmfdb_iso': '11616.s', 'p': 97, 'prec': 20, 'unit': 32626077802728049194985354087150791302, 'val': 1}