Elliptic curve data - 69828.z1

Formats: - HTML - YAML - JSON - 2024-05-01T08:26:00.214311

• 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': '69828bb', 'Clabel': '69828bb2', 'Cnumber': 2, 'abc_quality': 0.8915933416516306, 'absD': 33796752, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 1518, 'ainvs': [0, 1, 0, -1418, 20085], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 23], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 69828, 'degree': 31104, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.47533020246230773264782797724', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 25, 'isogeny_degrees': [1, 3], 'jinv': [37280608000, 3993], 'lmfdb_iso': '69828.z', 'lmfdb_label': '69828.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1418, 20085], 'min_quad_twist_disc': 1, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '66.8.0.b.1', '69.8.0-3.a.1.1', '1518.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6936130851693906885590356683', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27830122704586565229237486855', 'prec': 107}, 'szpiro_ratio': 2.9931812620485614, '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, 4, 0, 1, 0, 1, 0, 2, 0, 0, 0, 3, 0, -2, 0], 'aplist': [0, 1, 0, 4, 1, 2, 3, -2, 0, 3, -1, -11, -6, 10, -12, -12, 0, -14, 4, -6, -4, -8, 3, 6, 1], 'class_deg': 3, 'class_size': 2, 'conductor': 69828, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '69828.z', 'trace_hash': 705478925577196017}
• 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': '0.38648570209508213030425911132', 'prec': 103}, 'conductor': 69828, 'gens': [[21, 3, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6936130851693906885590356683', 'prec': 100}], 'lmfdb_label': '69828.z1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.9871728956665025056317299227', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.096506055784211074417956782193599403', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': [21]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [3, 1, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': 'a', '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '69828.z1'}
• ec_torsion_growth •

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

  
  
  • id: 3320712
    {'degree': 2, 'field': [-17, -1, 1], 'lmfdb_label': '69828.z1', 'torsion': [3]}
  • id: 3320713
    {'degree': 3, 'field': [-75, -38, -1, 1], 'lmfdb_label': '69828.z1', 'torsion': [2]}
  • id: 3320716
    {'degree': 6, 'field': [-159, -141, 229, 8, -36, -1, 1], 'lmfdb_label': '69828.z1', 'torsion': [6]}
  • id: 3320714
    {'degree': 6, 'field': [67, -423, 375, 95, -45, -3, 1], 'lmfdb_label': '69828.z1', 'torsion': [2, 2]}
  • id: 3320715
    {'degree': 6, 'field': [828, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '69828.z1', 'torsion': [3]}
  • id: 3320719
    {'degree': 12, 'field': [-891, 6237, 1398, -19920, 9442, 11000, -6632, -1913, 1301, 73, -68, -1, 1], 'lmfdb_label': '69828.z1', 'torsion': [2, 6]}
  • id: 3320717
    {'degree': 12, 'field': [157113, 0, -312110, 0, -198375, 0, -13570, 0, -1150, 0, 0, 0, 1], 'lmfdb_label': '69828.z1', 'torsion': [4]}
  • id: 3320718
    {'degree': 12, 'field': [687241, -4974, -12399, 33070, -12330, -5094, 1797, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '69828.z1', 'torsion': [3, 3]}
  • id: 3320720
    {'degree': 18, 'field': [-2167109043, 40013745552, 76120932591, 84148725153, 34185160593, -2069549415, -2733873197, 146795229, 53962743, -18777738, 5327214, 1062693, -426053, -43191, 11175, 942, -141, -9, 1], 'lmfdb_label': '69828.z1', 'torsion': [9]}
  • id: 3320721
    {'degree': 18, 'field': [4836036987, -1815100569, 1941155604, -278777232, 209090565, -92309031, 45751452, -13989627, 5100228, -1335073, 544230, -165771, 41220, -7875, 2313, -516, 90, -9, 1], 'lmfdb_label': '69828.z1', '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: 1691741
    {'conductor': 69828, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '69828.z1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1691742
    {'conductor': 69828, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '69828.z1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1691743
    {'conductor': 69828, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '69828.z1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1691744
    {'conductor': 69828, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '69828.z1', 'prime': 23, 'reduction_type': 0, '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: 2126155
    {'adelic_gens': [[3, 4, 8, 11], [4, 3, 9, 7], [1, 0, 6, 1], [1268, 255, 1, 760], [1257, 2, 142, 7], [277, 6, 831, 19], [1513, 6, 1512, 7], [1, 6, 0, 1]], 'adelic_image': '1518.16.0.?', 'conductor': 69828, 'lmfdb_label': '69828.z1', 'prime': 0}
  • id: 291302
    {'conductor': 69828, 'elladic_image': '3.4.0.1', 'lmfdb_label': '69828.z1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 3577861
    {'lmfdb_iso': '69828.z', 'p': 7, 'prec': 20, 'unit': 5633310049111443, 'val': 1}
  • id: 3577865
    {'lmfdb_iso': '69828.z', 'p': 13, 'prec': 20, 'unit': 577620854465468437167, 'val': 1}
  • id: 3577867
    {'lmfdb_iso': '69828.z', 'p': 17, 'prec': 20, 'unit': 177619617154393308509963, 'val': 1}
  • id: 3577868
    {'lmfdb_iso': '69828.z', 'p': 19, 'prec': 20, 'unit': 311531121034629425544124, 'val': 1}
  • id: 3577864
    {'lmfdb_iso': '69828.z', 'p': 29, 'prec': 20, 'unit': 5458675961611448674335928741, 'val': 1}
  • id: 3577875
    {'lmfdb_iso': '69828.z', 'p': 31, 'prec': 20, 'unit': 4394299806399867614799723459, 'val': 1}
  • id: 3577860
    {'lmfdb_iso': '69828.z', 'p': 37, 'prec': 20, 'unit': 298706109004452788893331368309, 'val': 1}
  • id: 3577862
    {'lmfdb_iso': '69828.z', 'p': 41, 'prec': 20, 'unit': 2220238062711952703311618988037, 'val': 1}
  • id: 3577863
    {'lmfdb_iso': '69828.z', 'p': 43, 'prec': 20, 'unit': 2795872945838978362138867245646, 'val': 1}
  • id: 3577866
    {'lmfdb_iso': '69828.z', 'p': 47, 'prec': 20, 'unit': 15132063714122029884344665176415, 'val': 1}
  • id: 3577869
    {'lmfdb_iso': '69828.z', 'p': 53, 'prec': 20, 'unit': 111065694203473616034283147469948, 'val': 1}
  • id: 3577874
    {'lmfdb_iso': '69828.z', 'p': 61, 'prec': 20, 'unit': 7389180959193868874009893835259173, 'val': 1}
  • id: 3577859
    {'lmfdb_iso': '69828.z', 'p': 67, 'prec': 20, 'unit': 24748108340943875038446662040588417, 'val': 1}
  • id: 3577872
    {'lmfdb_iso': '69828.z', 'p': 71, 'prec': 20, 'unit': 104904032025352519103904215915544283, 'val': 1}
  • id: 3577870
    {'lmfdb_iso': '69828.z', 'p': 73, 'prec': 20, 'unit': 102836638188735031985736878061771757, 'val': 1}
  • id: 3577873
    {'lmfdb_iso': '69828.z', 'p': 79, 'prec': 20, 'unit': 195183005989630081628544198556787133, 'val': 1}
  • id: 3577858
    {'lmfdb_iso': '69828.z', 'p': 83, 'prec': 20, 'unit': 1224578148989376112141650551756949691, 'val': 1}
  • id: 3577871
    {'lmfdb_iso': '69828.z', 'p': 89, 'prec': 20, 'unit': 9415173553531523472762338133296081621, 'val': 1}
  • id: 3577857
    {'lmfdb_iso': '69828.z', 'p': 97, 'prec': 20, 'unit': 5227316120050622913269509890587024537524, 'val': -1}