Elliptic curve data - 28665.j4

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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': '28665y', 'Clabel': '28665y1', 'Cnumber': 1, 'abc_quality': 0.8051938122534258, 'absD': 3160910389455, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 10920, 'ainvs': [1, -1, 1, 2857, 61422], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 28665, 'degree': 36864, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0846126956757656422203878592', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4], 'jinv': [30080231, 36855], 'lmfdb_iso': '28665.j', 'lmfdb_label': '28665.j4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 6, 7], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '56.12.0-4.c.1.5', '60.12.0-4.c.1.2', '312.12.0.?', '520.12.0.?', '840.24.0.?', '910.6.0.?', '1092.12.0.?', '1560.24.0.?', '1820.12.0.?', '2184.24.0.?', '3640.24.0.?', '5460.24.0.?', '10920.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.4547325459779590250144930190', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 8, 3185], [5, 6, 5733], [7, 32, 585], [13, 14, 2205]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.43764852318594585602991113098', 'prec': 107}, 'szpiro_ratio': 3.468364750204343, '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, -1, 0, -1, -1, 0, 0, 3, 0, 1, 0, 0, -1, 0, 0, -1, 2, 0, -4, 1], 'aplist': [-1, 0, -1, 0, 0, -1, 2, -4, -8, -6, 0, 2, 6, -8, 4, 6, -4, 10, 12, 4, 6, -8, 0, 6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 28665, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '28665.j', 'trace_hash': 870022736790593224}
• 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': '0.11426609414354799454052718664', 'prec': 103}, 'conductor': 28665, 'gens': [[30, 401, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.4547325459779590250144930190', 'prec': 100}], 'lmfdb_label': '28665.j4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.53438101479574418356438834594', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6235249379436850222117190518012550687', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-19, 9, 1]], 'xcoord_integral_points': [-19, 30, 62]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '28665.j4'}
• ec_torsion_growth •

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

  
  
  • id: 1437556
    {'degree': 2, 'field': [-68, -1, 1], 'lmfdb_label': '28665.j4', 'torsion': [4]}
  • id: 1437557
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '28665.j4', 'torsion': [4]}
  • id: 1437555
    {'degree': 2, 'field': [114, -1, 1], 'lmfdb_label': '28665.j4', 'torsion': [2, 2]}
  • id: 1437558
    {'degree': 4, 'field': [2094, -183, 25, -1, 1], 'lmfdb_label': '28665.j4', 'torsion': [2, 4]}
  • id: 1437560
    {'degree': 8, 'field': [-972, 5616, 1644, -1248, -743, -156, -5, 0, 1], 'lmfdb_label': '28665.j4', 'torsion': [8]}
  • id: 1437561
    {'degree': 8, 'field': [29761, -16307, 7365, -1742, 434, -58, 25, -3, 1], 'lmfdb_label': '28665.j4', 'torsion': [8]}
  • id: 1437562
    {'degree': 8, 'field': [60925, -61390, -27614, 6971, 1765, -295, -20, -4, 1], 'lmfdb_label': '28665.j4', 'torsion': [6]}
  • id: 1437559
    {'degree': 8, 'field': [33454656, 0, -1259472, 0, 21964, 0, -163, 0, 1], 'lmfdb_label': '28665.j4', 'torsion': [2, 4]}
  • id: 1437568
    {'degree': 16, 'field': [1221775, -1002700, -90975, 889435, 2017286, -2057991, 801094, -48790, -81540, 31934, 6841, -9249, 2870, -395, 24, -4, 1], 'lmfdb_label': '28665.j4', 'torsion': [12]}
  • id: 1437564
    {'degree': 16, 'field': [4384836, 0, -6118188, 0, 3294589, 0, -868257, 0, 125559, 0, -8762, 0, 207, 0, 15, 0, 1], 'lmfdb_label': '28665.j4', 'torsion': [2, 8]}
  • id: 1437565
    {'degree': 16, 'field': [70533376, -137579904, 110698816, -41859904, 5537344, 2044576, -1436356, 560702, -192621, 32867, 7849, -6350, 1762, -212, 15, -5, 1], 'lmfdb_label': '28665.j4', 'torsion': [2, 8]}
  • id: 1437567
    {'degree': 16, 'field': [6478157169, 0, -12084293853, 0, 453150000, 0, -42800346, 0, -1541970, 0, 51231, 0, -2232, 0, 0, 0, 1], 'lmfdb_label': '28665.j4', 'torsion': [12]}
  • id: 1437563
    {'degree': 16, 'field': [8081290816, -92049188992, 524238849152, 15394639616, 4115410928, -23366239136, 13844637024, -2872334432, 331449948, -21556984, 2599256, -420128, 43893, -1318, 18, -6, 1], 'lmfdb_label': '28665.j4', 'torsion': [4, 4]}
  • id: 1437566
    {'degree': 16, 'field': [23066015625, 0, 17712421875, 0, 5745937500, 0, 157443750, 0, 1518750, 0, -116625, 0, -2700, 0, 0, 0, 1], 'lmfdb_label': '28665.j4', 'torsion': [2, 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: 665709
    {'conductor': 28665, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '28665.j4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 665710
    {'conductor': 28665, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '28665.j4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 665711
    {'conductor': 28665, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '28665.j4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 665712
    {'conductor': 28665, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '28665.j4', 'prime': 13, '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: 1855678
    {'adelic_gens': [[1, 8, 0, 1], [3112, 10917, 4675, 10918], [1, 0, 8, 1], [6833, 6828, 6830, 1367], [7279, 10912, 7276, 10887], [4376, 3, 5, 2], [1, 4, 4, 17], [7, 6, 10914, 10915], [10913, 8, 10912, 9], [5884, 1, 9263, 6], [4099, 4098, 1378, 6835]], 'adelic_image': '10920.48.0.?', 'conductor': 28665, 'lmfdb_label': '28665.j4', 'prime': 0}
  • id: 129680
    {'conductor': 28665, 'elladic_image': '4.6.0.1', 'lmfdb_label': '28665.j4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1380907
    {'lmfdb_iso': '28665.j', 'p': 17, 'prec': 20, 'unit': 199463585966092175399171, 'val': 1}
  • id: 1380908
    {'lmfdb_iso': '28665.j', 'p': 19, 'prec': 20, 'unit': 1837962409034941672269068, 'val': 1}
  • id: 1380912
    {'lmfdb_iso': '28665.j', 'p': 23, 'prec': 20, 'unit': 12149608954098109622255475, 'val': 1}
  • id: 1380905
    {'lmfdb_iso': '28665.j', 'p': 29, 'prec': 20, 'unit': 4822773288424495571137718482, 'val': 1}
  • id: 1380901
    {'lmfdb_iso': '28665.j', 'p': 37, 'prec': 20, 'unit': 313411242143772382274232706363, 'val': 1}
  • id: 1380903
    {'lmfdb_iso': '28665.j', 'p': 41, 'prec': 20, 'unit': 373534602384260695230223842344, 'val': 1}
  • id: 1380904
    {'lmfdb_iso': '28665.j', 'p': 43, 'prec': 20, 'unit': 4691298970664037652064608587903, 'val': 1}
  • id: 1380914
    {'lmfdb_iso': '28665.j', 'p': 47, 'prec': 20, 'unit': 30474787160370879323245723821311, 'val': 1}
  • id: 1380909
    {'lmfdb_iso': '28665.j', 'p': 53, 'prec': 20, 'unit': 326492080049502207922751988099338, 'val': 1}
  • id: 1380910
    {'lmfdb_iso': '28665.j', 'p': 59, 'prec': 20, 'unit': 3349496242876801802541247685229227, 'val': 1}
  • id: 1380915
    {'lmfdb_iso': '28665.j', 'p': 61, 'prec': 20, 'unit': 3858726623018962300714316688885811, 'val': 1}
  • id: 1380900
    {'lmfdb_iso': '28665.j', 'p': 67, 'prec': 20, 'unit': 22065892072754577746783051459083632, 'val': 1}
  • id: 1380902
    {'lmfdb_iso': '28665.j', 'p': 71, 'prec': 20, 'unit': 120218141675896787883728501470533022, 'val': 1}
  • id: 1380911
    {'lmfdb_iso': '28665.j', 'p': 73, 'prec': 20, 'unit': 122112875108883088255443238463242632, 'val': 1}
  • id: 1380906
    {'lmfdb_iso': '28665.j', 'p': 79, 'prec': 20, 'unit': 730521362294348926589012286355814166, 'val': 1}
  • id: 1380913
    {'lmfdb_iso': '28665.j', 'p': 89, 'prec': 20, 'unit': 6417926729656450205855202438383421272, 'val': 1}
  • id: 1380899
    {'lmfdb_iso': '28665.j', 'p': 97, 'prec': 20, 'unit': 39265660151241077444708540669563016258, 'val': 1}