Elliptic curve data - 121296.cs3

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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': '121296cm', 'Clabel': '121296cm2', 'Cnumber': 2, 'abc_quality': 0.9724335123602292, 'absD': 61459233470208, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1596, 'ainvs': [0, 1, 0, -10228, -130936], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 121296, 'degree': 331776, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3377223077004912878966600359', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 70, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [9826000, 5103], 'lmfdb_iso': '121296.cs', 'lmfdb_label': '121296.cs3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -28, -28], 'min_quad_twist_disc': 76, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0.j.1', '28.6.0.a.1', '84.48.1.?', '228.48.0.?', '798.24.0.?', '1596.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.59659530225602581505267509435', 'prec': 107}, 'szpiro_ratio': 3.3583111528563605, '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, 1, 0, 0, 0, -1, 0, 1, 0, 6, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 1, 0, -1, 6, -2, 0, 0, 6, -6, 8, -2, -12, 4, -12, 6, 0, -10, 8, 6, -10, -4, 12, -12, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 121296, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '121296.cs', 'trace_hash': 1343964610261662161}
• 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': '0.068876198167365423080146107271', 'prec': 107}, 'conductor': 121296, 'gens': [], 'heights': [], 'lmfdb_label': '121296.cs3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.50249320700847359494888150202', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0149592420508415696932890121023895549', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-13, 0, 1]], 'xcoord_integral_points': [-13]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '7': [0, 0], '19': 'a'}, 'iwp0': 5, 'lmfdb_label': '121296.cs3'}
• ec_torsion_growth •

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

  
  
  • id: 5540950
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '121296.cs3', 'torsion': [6]}
  • id: 5540949
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '121296.cs3', 'torsion': [2, 2]}
  • id: 5540952
    {'degree': 4, 'field': [9, 0, -13, 0, 1], 'lmfdb_label': '121296.cs3', 'torsion': [2, 6]}
  • id: 5540951
    {'degree': 4, 'field': [2527, 0, -95, 0, 1], 'lmfdb_label': '121296.cs3', 'torsion': [4]}
  • id: 5540953
    {'degree': 6, 'field': [6021, 2394, -323, -126, 19, 0, 1], 'lmfdb_label': '121296.cs3', 'torsion': [6]}
  • id: 5540954
    {'degree': 8, 'field': [-6044, 44768, -6480, 2312, 404, 32, -132, -4, 1], 'lmfdb_label': '121296.cs3', 'torsion': [2, 4]}
  • id: 5540955
    {'degree': 8, 'field': [15876, 21168, 32760, -6552, 1086, 264, -32, -2, 1], 'lmfdb_label': '121296.cs3', 'torsion': [2, 4]}
  • id: 5540956
    {'degree': 8, 'field': [84661, -13262, -1478, -1246, 434, 134, -38, -2, 1], 'lmfdb_label': '121296.cs3', 'torsion': [12]}
  • id: 5540957
    {'degree': 12, 'field': [28317141, 5853114, -5203619, -1278636, 587278, 65642, -27083, 4214, -740, -220, 55, -6, 1], 'lmfdb_label': '121296.cs3', 'torsion': [3, 6]}
  • id: 5540958
    {'degree': 12, 'field': [32558436, 0, 90432, 0, 321364, 0, -1387, 0, 855, 0, -1, 0, 1], 'lmfdb_label': '121296.cs3', 'torsion': [2, 6]}
  • id: 5540961
    {'degree': 16, 'field': [700569, 457002, 664722, 99000, 246057, 47118, 36010, 12038, 3456, 1612, 296, 30, 149, -44, 24, -4, 1], 'lmfdb_label': '121296.cs3', 'torsion': [2, 12]}
  • id: 5540960
    {'degree': 16, 'field': [1178577, 2505060, -1105584, -2412564, 307022, 900064, -24176, -193308, -1217, 26576, 528, -2428, -202, 252, -16, -8, 1], 'lmfdb_label': '121296.cs3', 'torsion': [2, 12]}
  • id: 5540959
    {'degree': 16, 'field': [736878657, 210111252, -483829308, 24440136, 176352454, -117588916, 32952224, -1361148, -1702397, 495028, 25168, -51476, 7750, 912, -172, -4, 1], 'lmfdb_label': '121296.cs3', 'torsion': [8]}
  • id: 5540962
    {'degree': 18, 'field': [-261843234183, -77524349616, 125855085249, 35302899106, -26247955137, -6916904958, 3140244958, 753235746, -242074482, -50491466, 12673071, 2164356, -455837, -58308, 10905, 898, -156, -6, 1], 'lmfdb_label': '121296.cs3', 'torsion': [18]}
• 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: 2985514
    {'conductor': 121296, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '121296.cs3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2985515
    {'conductor': 121296, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '121296.cs3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 2985516
    {'conductor': 121296, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '121296.cs3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2985517
    {'conductor': 121296, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '121296.cs3', 'prime': 19, '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: 2455463
    {'adelic_gens': [[1585, 12, 1584, 13], [587, 0, 0, 1595], [930, 779, 931, 1462], [58, 171, 969, 1084], [1, 0, 12, 1], [1, 6, 6, 37], [11, 2, 1546, 1587], [1, 12, 0, 1], [989, 1178, 228, 1]], 'adelic_image': '1596.96.1.?', 'conductor': 121296, 'lmfdb_label': '121296.cs3', 'prime': 0}
  • id: 475925
    {'conductor': 121296, 'elladic_image': '2.3.0.1', 'lmfdb_label': '121296.cs3', 'modell_image': '2B', 'prime': 2}
  • id: 475926
    {'conductor': 121296, 'elladic_image': '3.4.0.1', 'lmfdb_label': '121296.cs3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 121296.cs does not appear in ec_padic