Elliptic curve data - 8400.p1

Formats: - HTML - YAML - JSON - 2024-06-03T09:35:04.237929

• 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': '8400bp', 'Clabel': '8400bp5', 'Cnumber': 5, 'abc_quality': 1.0369284989490737, 'absD': 201600000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, -1, 0, -6720008, 6707302512], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 8400, 'degree': 147456, 'elladic_images': ['16.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2346235662511274501790388361', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [524388516989299201, 3150], 'lmfdb_iso': '8400.p', 'lmfdb_label': '8400.p1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -16800, -845133], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0.e.1', '20.12.0-4.c.1.2', '24.24.0-8.n.1.4', '40.24.0-8.n.1.1', '48.48.0-16.e.1.2', '56.24.0.bh.1', '80.48.0.?', '112.48.0.?', '120.48.0.?', '168.48.0.?', '240.96.0.?', '280.48.0.?', '336.96.0.?', '560.96.0.?', '840.96.0.?', '1680.192.1.?'], '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': '0.92648169083736596886718417269', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.73675742947413195346142704803', 'prec': 103}, 'szpiro_ratio': 6.504591362196844, '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, -4, 0, 2, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, -1, 0, 1, -4, 2, -2, 4, -8, 6, 8, 2, 2, -12, -8, -6, -4, -2, 12, -8, 14, 0, 12, 2, -10], 'class_deg': 8, 'class_size': 6, 'conductor': 8400, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '8400.p', 'trace_hash': 1625614557540898145}
• 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': '0.011455937407583796423773590337', 'prec': 107}, 'conductor': 8400, 'gens': [[1452, 3000, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.92648169083736596886718417269', 'prec': 103}], 'lmfdb_label': '8400.p1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.48869007813480689083155259852', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6220992790862430143551589163123857143', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[1497, 0, 1]], 'xcoord_integral_points': [1452, 1497, 1722]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': [2, 0], '11': [1, 0], '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': '8400.p1'}
• ec_torsion_growth •

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

  
  
  • id: 439275
    {'degree': 2, 'field': [-70, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [4]}
  • id: 439273
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [2, 2]}
  • id: 439274
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '8400.p1', 'torsion': [4]}
  • id: 439277
    {'degree': 4, 'field': [1, 8, -7, -2, 1], 'lmfdb_label': '8400.p1', 'torsion': [8]}
  • id: 439276
    {'degree': 4, 'field': [155, 30, -29, -2, 1], 'lmfdb_label': '8400.p1', 'torsion': [2, 4]}
  • id: 439278
    {'degree': 4, 'field': [1639, 86, -85, -2, 1], 'lmfdb_label': '8400.p1', 'torsion': [8]}
  • id: 439281
    {'degree': 8, 'field': [-671, 3420, -2504, -1772, 737, 176, -54, -4, 1], 'lmfdb_label': '8400.p1', 'torsion': [2, 8]}
  • id: 439283
    {'degree': 8, 'field': [-75, 0, 820, 0, 30, 0, 0, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [6]}
  • id: 439279
    {'degree': 8, 'field': [10201, 0, 8060, 0, -102, 0, 20, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [2, 4]}
  • id: 439280
    {'degree': 8, 'field': [15876, 0, 0, 0, -28, 0, 0, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [8]}
  • id: 439282
    {'degree': 8, 'field': [27481, 10924, -9568, -2648, 1165, 188, -58, -4, 1], 'lmfdb_label': '8400.p1', 'torsion': [16]}
  • id: 439287
    {'degree': 16, 'field': [-324119, -3695356, 3960080, 35505780, 38689064, -457016, -15327968, -2637900, 2282161, 457824, -165548, -29932, 6314, 828, -124, -8, 1], 'lmfdb_label': '8400.p1', 'torsion': [2, 16]}
  • id: 439285
    {'degree': 16, 'field': [9801, 0, 101484, 0, 34078, 0, -10944, 0, 1343, 0, 312, 0, 2, 0, 12, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [2, 8]}
  • id: 439289
    {'degree': 16, 'field': [452225, -512600, 588100, 1920, -361670, 372680, -24944, -82568, 16275, 4840, -2992, 1208, -262, 0, 20, -8, 1], 'lmfdb_label': '8400.p1', 'torsion': [12]}
  • id: 439284
    {'degree': 16, 'field': [224850025, 0, 72037740, 0, -4576514, 0, -946368, 0, 95199, 0, 1656, 0, -446, 0, 12, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [4, 4]}
  • id: 439286
    {'degree': 16, 'field': [1944810000, 0, 0, 0, -537138000, 0, 0, 0, 148308300, 0, 0, 0, -12180, 0, 0, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [16]}
  • id: 439288
    {'degree': 16, 'field': [3102601401, 0, -10114632, 0, 107619948, 0, -30068384, 0, 2788430, 0, -150344, 0, 5548, 0, -112, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [2, 6]}
  • id: 439290
    {'degree': 16, 'field': [4596433209, 0, 515773332, 0, -91985220, 0, -5800896, 0, 549690, 0, 12196, 0, -1032, 0, 0, 0, 1], 'lmfdb_label': '8400.p1', 'torsion': [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: 175006
    {'conductor': 8400, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '8400.p1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 175007
    {'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8400.p1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 175008
    {'conductor': 8400, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '8400.p1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 175009
    {'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8400.p1', 'prime': 7, '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: 1719589
    {'adelic_gens': [[5, 4, 1676, 1677], [428, 425, 843, 842], [1, 16, 0, 1], [1665, 16, 1664, 17], [15, 2, 1582, 1667], [496, 5, 915, 1666], [1133, 16, 304, 1365], [1, 0, 16, 1], [202, 1255, 1467, 838], [659, 1664, 592, 315]], 'adelic_image': '1680.192.1.?', 'conductor': 8400, 'lmfdb_label': '8400.p1', 'prime': 0}
  • id: 41191
    {'conductor': 8400, 'elladic_image': '16.24.0.1', 'lmfdb_label': '8400.p1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 347652
    {'lmfdb_iso': '8400.p', 'p': 11, 'prec': 20, 'unit': 40259954714997254481, 'val': 1}
  • id: 347658
    {'lmfdb_iso': '8400.p', 'p': 13, 'prec': 20, 'unit': 106355428334660275221, 'val': 1}
  • id: 347660
    {'lmfdb_iso': '8400.p', 'p': 17, 'prec': 20, 'unit': 136097653915914795369112, 'val': 1}
  • id: 347661
    {'lmfdb_iso': '8400.p', 'p': 19, 'prec': 20, 'unit': 1559788588417184710934082, 'val': 1}
  • id: 347664
    {'lmfdb_iso': '8400.p', 'p': 23, 'prec': 20, 'unit': 60917420546150781141896911, 'val': 1}
  • id: 347657
    {'lmfdb_iso': '8400.p', 'p': 29, 'prec': 20, 'unit': 5022339600625889130120330632, 'val': 1}
  • id: 347669
    {'lmfdb_iso': '8400.p', 'p': 31, 'prec': 20, 'unit': 17570206983084334892542509754, 'val': 1}
  • id: 347653
    {'lmfdb_iso': '8400.p', 'p': 37, 'prec': 20, 'unit': 330798064243449532407949947382, 'val': 1}
  • id: 347655
    {'lmfdb_iso': '8400.p', 'p': 41, 'prec': 20, 'unit': 3761167222839918962598801774690, 'val': 1}
  • id: 347656
    {'lmfdb_iso': '8400.p', 'p': 43, 'prec': 20, 'unit': 8421531313177958458773296549949, 'val': 1}
  • id: 347659
    {'lmfdb_iso': '8400.p', 'p': 47, 'prec': 20, 'unit': 17083973144811561866503686110621, 'val': 1}
  • id: 347662
    {'lmfdb_iso': '8400.p', 'p': 53, 'prec': 20, 'unit': 73032140605062954062070475965027, 'val': 1}
  • id: 347666
    {'lmfdb_iso': '8400.p', 'p': 59, 'prec': 20, 'unit': 1187737749254677148099138493378686, 'val': 1}
  • id: 347667
    {'lmfdb_iso': '8400.p', 'p': 61, 'prec': 20, 'unit': 7388218186530759562586029308885688, 'val': 1}
  • id: 347651
    {'lmfdb_iso': '8400.p', 'p': 67, 'prec': 20, 'unit': 25085680766448633955686787621871515, 'val': 1}
  • id: 347654
    {'lmfdb_iso': '8400.p', 'p': 71, 'prec': 20, 'unit': 48738739355062173068121258885764598, 'val': 1}
  • id: 347663
    {'lmfdb_iso': '8400.p', 'p': 73, 'prec': 20, 'unit': 78920407025362613334237968644050587, 'val': 1}
  • id: 347668
    {'lmfdb_iso': '8400.p', 'p': 83, 'prec': 20, 'unit': 1251627283851673210242089019082231752, 'val': 1}
  • id: 347665
    {'lmfdb_iso': '8400.p', 'p': 89, 'prec': 20, 'unit': 9179424500955220501751933502622339065, 'val': 1}
  • id: 347650
    {'lmfdb_iso': '8400.p', 'p': 97, 'prec': 20, 'unit': 35630346853086515108829640942195275551, 'val': 1}