Elliptic curve data - 19536.c2

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

  
  {'Ciso': '19536g', 'Clabel': '19536g4', 'Cnumber': 4, 'abc_quality': 0.9871996871198981, 'absD': 1070178969034847232, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3256, 'ainvs': [0, -1, 0, -597624, -170517312], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 37], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 19536, 'degree': 208896, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2216170596139264271620611234', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [23051997945147370468, 1045096649448093], 'lmfdb_iso': '19536.c', 'lmfdb_label': '19536.c2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -597624, 170517312], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '74.6.0.?', '88.24.0.?', '148.24.0.?', '3256.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.7467502143731023898739824809', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 37], [3, 4, 592], [11, 12, 1776], [37, 38, 528]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6439944091473053359810343555', 'prec': 100}, 'szpiro_ratio': 5.214137844352074, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 0, 2, 0, 2, 0, 6, 0, 0, 0], 'aplist': [0, -1, -2, 0, 1, 2, 6, 0, 0, 2, 0, 1, 2, 0, -8, -10, -12, 2, 4, 8, -6, -4, 4, -6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 19536, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '19536.c', 'trace_hash': 1053955318969286744}
• 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': '0.011757850671693544158957762471', 'prec': 107}, 'conductor': 19536, 'gens': [[1428, 43428, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.7467502143731023898739824809', 'prec': 100}], 'lmfdb_label': '19536.c2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.17219054255540081534897521475', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8709297133948128882339905829957512877', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-442, 2662, 1]], 'xcoord_integral_points': [-442, 889, 1428]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [2, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '19536.c2'}
• ec_torsion_growth •

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

  
  
  • id: 998606
    {'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '19536.c2', 'torsion': [2, 4]}
  • id: 998607
    {'degree': 4, 'field': [148, 0, 14, 0, 1], 'lmfdb_label': '19536.c2', 'torsion': [8]}
  • id: 998611
    {'degree': 8, 'field': [-3468, 0, 1540, 0, -204, 0, 0, 0, 1], 'lmfdb_label': '19536.c2', 'torsion': [12]}
  • id: 998609
    {'degree': 8, 'field': [2304, 0, -1472, 0, 468, 0, 6, 0, 1], 'lmfdb_label': '19536.c2', 'torsion': [2, 8]}
  • id: 998608
    {'degree': 8, 'field': [111556, 0, -3992, 0, 672, 0, 4, 0, 1], 'lmfdb_label': '19536.c2', 'torsion': [4, 4]}
  • id: 998610
    {'degree': 8, 'field': [11602321, 1915090, -1856722, -116282, 57007, 1358, -448, -4, 1], 'lmfdb_label': '19536.c2', 'torsion': [2, 8]}
  • id: 998613
    {'degree': 16, 'field': [729, 0, 76680, 0, -39330, 0, 2160, 0, -2505, 0, 1600, 0, -186, 0, 0, 0, 1], 'lmfdb_label': '19536.c2', 'torsion': [2, 12]}
  • id: 998612
    {'degree': 16, 'field': [11480407475625, 0, -1903058536500, 0, 85924214442, 0, -1274172108, 0, 108854518, 0, -1391052, 0, 32898, 0, -324, 0, 1], 'lmfdb_label': '19536.c2', '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: 442075
    {'conductor': 19536, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '19536.c2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 442076
    {'conductor': 19536, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '19536.c2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 442077
    {'conductor': 19536, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '19536.c2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 442078
    {'conductor': 19536, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '19536.c2', 'prime': 37, '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: 1794618
    {'adelic_gens': [[2961, 8, 2076, 33], [2820, 1, 3191, 6], [1, 0, 8, 1], [3249, 8, 3248, 9], [7, 6, 3250, 3251], [1213, 1220, 1174, 2843], [411, 410, 1234, 2859], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '3256.48.0.?', 'conductor': 19536, 'lmfdb_label': '19536.c2', 'prime': 0}
  • id: 91237
    {'conductor': 19536, 'elladic_image': '4.12.0.7', 'lmfdb_label': '19536.c2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 905713
    {'lmfdb_iso': '19536.c', 'p': 5, 'prec': 20, 'unit': 1313251713141, 'val': 1}
  • id: 905717
    {'lmfdb_iso': '19536.c', 'p': 13, 'prec': 20, 'unit': 146845472953121634422, 'val': 1}
  • id: 905719
    {'lmfdb_iso': '19536.c', 'p': 17, 'prec': 20, 'unit': 135409280517364364705954, 'val': 1}
  • id: 905716
    {'lmfdb_iso': '19536.c', 'p': 29, 'prec': 20, 'unit': 5187585459801391539693195714, 'val': 1}
  • id: 905715
    {'lmfdb_iso': '19536.c', 'p': 41, 'prec': 20, 'unit': 877982175826427758502840625145, 'val': 1}
  • id: 905725
    {'lmfdb_iso': '19536.c', 'p': 47, 'prec': 20, 'unit': 25298673498306601308879606638413, 'val': 1}
  • id: 905721
    {'lmfdb_iso': '19536.c', 'p': 53, 'prec': 20, 'unit': 481985588100674353788540151720065, 'val': 1}
  • id: 905722
    {'lmfdb_iso': '19536.c', 'p': 59, 'prec': 20, 'unit': 1108437698805712749450518432935074, 'val': 1}
  • id: 905726
    {'lmfdb_iso': '19536.c', 'p': 61, 'prec': 20, 'unit': 4355384902236336485920155440639534, 'val': 1}
  • id: 905712
    {'lmfdb_iso': '19536.c', 'p': 67, 'prec': 20, 'unit': 49263869326675632716827647766831599, 'val': 1}
  • id: 905714
    {'lmfdb_iso': '19536.c', 'p': 71, 'prec': 20, 'unit': 6885914882677736090636830042946571, 'val': 1}
  • id: 905723
    {'lmfdb_iso': '19536.c', 'p': 73, 'prec': 20, 'unit': 78775966109133619686797116600817149, 'val': 1}
  • id: 905718
    {'lmfdb_iso': '19536.c', 'p': 79, 'prec': 20, 'unit': 453404655788171823562111112822547965, 'val': 1}
  • id: 905720
    {'lmfdb_iso': '19536.c', 'p': 83, 'prec': 20, 'unit': 1813201410917152105493184404336595466, 'val': 1}
  • id: 905724
    {'lmfdb_iso': '19536.c', 'p': 89, 'prec': 20, 'unit': 2721713104697854559925126653183188038, 'val': 1}
  • id: 905711
    {'lmfdb_iso': '19536.c', 'p': 97, 'prec': 20, 'unit': 39896032940339200827314477336855118026, 'val': 1}