Elliptic curve data - 1216.e2

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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': '1216b', 'Clabel': '1216b1', 'Cnumber': 1, 'abc_quality': 0.9328072208159958, 'absD': 39845888, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 4104, 'ainvs': [0, -1, 0, -993, 12385], 'analytic_rank': 1, 'bad_primes': [2, 19], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 1216, 'degree': 384, 'elladic_images': ['27.36.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.42627809312905185368256486534', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 3, 9], 'jinv': [-413493625, 152], 'lmfdb_iso': '1216.e', 'lmfdb_label': '1216.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -16, 22], 'min_quad_twist_disc': 8, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '24.8.0-3.a.1.2', '27.36.0.a.1', '72.24.0.?', '114.8.0.?', '152.2.0.?', '171.36.0.?', '216.72.0.?', '342.72.0.?', '456.16.0.?', '513.324.16.?', '1026.648.16.?', '1368.144.3.?', '4104.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.27825869830453934329710178154', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 19], [19, 20, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61344267771086611044328331685', 'prec': 107}, 'szpiro_ratio': 4.549622927246401, '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, -1, 0, 0, 0, -1, 0, -2, 0, 6, 0, -5, 0, 0, 0, 3, 0, -1, 0], 'aplist': [0, -1, 0, -1, 6, -5, 3, -1, 3, -9, -4, -2, 0, -8, 0, 3, -9, 10, -5, -6, -7, -10, 6, -12, -10], 'class_deg': 9, 'class_size': 3, 'conductor': 1216, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '1216.e', 'trace_hash': 1980463916705955596}
• 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': '0.42632377496755428724183948498', 'prec': 103}, 'conductor': 1216, 'gens': [[9, 64, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.27825869830453934329710178154', 'prec': 103}], 'lmfdb_label': '1216.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.0053183057830649435951031330', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2319890458138393663961927064500415656', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [9, 19]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [3, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1216.e2'}
• ec_torsion_growth •

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

  
  
  • id: 60120
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '1216.e2', 'torsion': [3]}
  • id: 60121
    {'degree': 3, 'field': [-2, -2, -1, 1], 'lmfdb_label': '1216.e2', 'torsion': [2]}
  • id: 60124
    {'degree': 6, 'field': [-7, -32, 30, 34, -17, -2, 1], 'lmfdb_label': '1216.e2', 'torsion': [9]}
  • id: 60125
    {'degree': 6, 'field': [-1, 0, -2, -2, 2, 0, 1], 'lmfdb_label': '1216.e2', 'torsion': [6]}
  • id: 60122
    {'degree': 6, 'field': [16, 16, 34, 4, 5, -2, 1], 'lmfdb_label': '1216.e2', 'torsion': [2, 2]}
  • id: 60123
    {'degree': 6, 'field': [96, 0, 52, 0, 2, 0, 1], 'lmfdb_label': '1216.e2', 'torsion': [3]}
  • id: 60126
    {'degree': 12, 'field': [-4, 24, -42, 24, -20, 44, -25, -4, 1, 4, 5, -4, 1], 'lmfdb_label': '1216.e2', 'torsion': [4]}
  • id: 60129
    {'degree': 12, 'field': [4, 0, -14, 0, 1, 0, 24, 0, 23, 0, 8, 0, 1], 'lmfdb_label': '1216.e2', 'torsion': [2, 6]}
  • id: 60128
    {'degree': 12, 'field': [64, 0, 64, 0, -48, 0, -24, 0, 32, 0, -10, 0, 1], 'lmfdb_label': '1216.e2', 'torsion': [9]}
  • id: 60127
    {'degree': 12, 'field': [388, 1752, 2582, 864, -765, -168, 70, -216, 57, -12, 8, 0, 1], 'lmfdb_label': '1216.e2', 'torsion': [3, 3]}
  • id: 60131
    {'degree': 18, 'field': [-10952, 0, 5620, 0, 3492, 0, -1291, 0, -518, 0, 137, 0, 14, 0, -2, 0, -4, 0, 1], 'lmfdb_label': '1216.e2', 'torsion': [18]}
  • id: 60130
    {'degree': 18, 'field': [13824, 0, 37440, 0, 7200, 0, 26644, 0, -110, 0, 3625, 0, -4, 0, -125, 0, 0, 0, 1], 'lmfdb_label': '1216.e2', '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: 17823
    {'conductor': 1216, 'conductor_valuation': 6, 'discriminant_valuation': 21, 'j_denominator_valuation': 3, 'kodaira_symbol': -15, 'lmfdb_label': '1216.e2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 17824
    {'conductor': 1216, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1216.e2', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1672200
    {'adelic_gens': [[3227, 681, 2323, 2500], [31, 36, 2386, 1447], [1, 54, 0, 1], [2051, 4050, 2043, 3617], [28, 27, 729, 703], [1969, 18, 2101, 3595], [3079, 54, 0, 1], [4051, 54, 4050, 55], [1, 0, 54, 1]], 'adelic_image': '4104.1296.43.?', 'conductor': 1216, 'lmfdb_label': '1216.e2', 'prime': 0}
  • id: 5805
    {'conductor': 1216, 'elladic_image': '27.36.0.1', 'lmfdb_label': '1216.e2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 30084
    {'lmfdb_iso': '1216.e', 'p': 7, 'prec': 20, 'unit': 3717827384262008, 'val': 1}
  • id: 30082
    {'lmfdb_iso': '1216.e', 'p': 11, 'prec': 20, 'unit': 57042811036660784470, 'val': 1}
  • id: 30088
    {'lmfdb_iso': '1216.e', 'p': 13, 'prec': 20, 'unit': 72748753115194960616, 'val': 1}
  • id: 30090
    {'lmfdb_iso': '1216.e', 'p': 17, 'prec': 20, 'unit': 148392833013274037267568, 'val': 1}
  • id: 30093
    {'lmfdb_iso': '1216.e', 'p': 23, 'prec': 20, 'unit': 2643859329870533574020652, 'val': 1}
  • id: 30087
    {'lmfdb_iso': '1216.e', 'p': 29, 'prec': 20, 'unit': 4853543522354918509593811516, 'val': 1}
  • id: 30098
    {'lmfdb_iso': '1216.e', 'p': 31, 'prec': 20, 'unit': 16517488256999064855580007950, 'val': 1}
  • id: 30083
    {'lmfdb_iso': '1216.e', 'p': 37, 'prec': 20, 'unit': 179886220034638513012458748703, 'val': 1}
  • id: 30086
    {'lmfdb_iso': '1216.e', 'p': 43, 'prec': 20, 'unit': 7034026413345337475027754470040, 'val': 1}
  • id: 30092
    {'lmfdb_iso': '1216.e', 'p': 53, 'prec': 20, 'unit': 380168781459078972119009896287171, 'val': 1}
  • id: 30096
    {'lmfdb_iso': '1216.e', 'p': 59, 'prec': 20, 'unit': 19872227449963861025306766794578, 'val': 2}
  • id: 30097
    {'lmfdb_iso': '1216.e', 'p': 61, 'prec': 20, 'unit': 5106599790989163565572680212587162, 'val': 1}
  • id: 30081
    {'lmfdb_iso': '1216.e', 'p': 67, 'prec': 20, 'unit': 29848336494555615921153145960140692, 'val': 1}
  • id: 30095
    {'lmfdb_iso': '1216.e', 'p': 71, 'prec': 20, 'unit': 48183347052253253126584118096251861, 'val': 1}
  • id: 30085
    {'lmfdb_iso': '1216.e', 'p': 73, 'prec': 20, 'unit': 243562976706954060226772383072327553, 'val': 1}
  • id: 30089
    {'lmfdb_iso': '1216.e', 'p': 79, 'prec': 20, 'unit': 302127966810831753830170697725450892, 'val': 1}
  • id: 30091
    {'lmfdb_iso': '1216.e', 'p': 83, 'prec': 20, 'unit': 2609988265117277013251343142169177519, 'val': 1}
  • id: 30094
    {'lmfdb_iso': '1216.e', 'p': 89, 'prec': 20, 'unit': 10216075279359089603772303510120194958, 'val': 1}
  • id: 30080
    {'lmfdb_iso': '1216.e', 'p': 97, 'prec': 20, 'unit': 6894112862547809647184983038201488709, 'val': 1}