Elliptic curve data - 21021.e5

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

  
  {'Ciso': '21021b', 'Clabel': '21021b1', 'Cnumber': 1, 'abc_quality': 0.8840474094399083, 'absD': 110380997727, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 48048, 'ainvs': [1, 1, 1, -1177, -22786], 'analytic_rank': 0, 'bad_primes': [3, 7, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21021, 'degree': 24576, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.82090353287462616450520186547', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-1532808577, 938223], 'lmfdb_iso': '21021.e', 'lmfdb_label': '21021.e5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -24, 63], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '28.12.0-4.c.1.2', '48.24.0.g.1', '56.24.0-8.n.1.5', '88.24.0.?', '104.24.0.?', '286.6.0.?', '336.48.0.?', '528.48.0.?', '572.12.0.?', '616.48.0.?', '624.48.0.?', '728.48.0.?', '1144.48.0.?', '3696.96.0.?', '4004.24.0.?', '4368.96.0.?', '6864.96.1.?', '8008.96.0.?', '48048.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15205154165303048804747450625', 'prec': 107}, 'szpiro_ratio': 3.370489523442716, '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, -1, -1, 2, 1, 0, 3, 1, -2, -1, 1, -1, 0, -2, -1, 6, -1, 4, -2], 'aplist': [-1, -1, 2, 0, -1, -1, 6, 4, -8, -10, 0, 6, -10, 4, -8, -10, 12, -14, -12, 0, 6, 8, -12, -2, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 21021, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '21021.e', 'trace_hash': 2051298451983195990}
• 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': '0.19362982412935447326442411980', 'prec': 103}, 'conductor': 21021, 'gens': [], 'heights': [], 'lmfdb_label': '21021.e5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.39649332660565027435842870442', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.79298665321130054871685740884702106333', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[41, -21, 1]], 'xcoord_integral_points': [41]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [0, 0], '7': 'a', '11': [0, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '21021.e5'}
• ec_torsion_growth •

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

  
  
  • id: 1070039
    {'degree': 2, 'field': [-250, -1, 1], 'lmfdb_label': '21021.e5', 'torsion': [4]}
  • id: 1070040
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '21021.e5', 'torsion': [4]}
  • id: 1070038
    {'degree': 2, 'field': [36, -1, 1], 'lmfdb_label': '21021.e5', 'torsion': [2, 2]}
  • id: 1070042
    {'degree': 4, 'field': [1, 0, 9, 0, 1], 'lmfdb_label': '21021.e5', 'torsion': [8]}
  • id: 1070043
    {'degree': 4, 'field': [25, 0, -3, 0, 1], 'lmfdb_label': '21021.e5', 'torsion': [8]}
  • id: 1070041
    {'degree': 4, 'field': [1156, 0, 75, 0, 1], 'lmfdb_label': '21021.e5', 'torsion': [2, 4]}
  • id: 1070046
    {'degree': 8, 'field': [1472, 752, -660, -190, 111, -22, 12, -4, 1], 'lmfdb_label': '21021.e5', 'torsion': [2, 8]}
  • id: 1070047
    {'degree': 8, 'field': [3047, -12296, 12278, 35, -14, -7, 7, -4, 1], 'lmfdb_label': '21021.e5', 'torsion': [6]}
  • id: 1070045
    {'degree': 8, 'field': [17161, 0, -16386, 0, 5363, 0, -150, 0, 1], 'lmfdb_label': '21021.e5', 'torsion': [8]}
  • id: 1070044
    {'degree': 8, 'field': [36864, 0, 10640, 0, 580, 0, -28, 0, 1], 'lmfdb_label': '21021.e5', 'torsion': [2, 4]}
  • id: 1070054
    {'degree': 16, 'field': [5041, 0, -3892, 0, -3128, 0, 4137, 0, 2328, 0, 231, 0, 85, 0, 14, 0, 1], 'lmfdb_label': '21021.e5', 'torsion': [12]}
  • id: 1070048
    {'degree': 16, 'field': [760384, 0, 2136352, 0, 410164, 0, -91416, 0, 10353, 0, 936, 0, -38, 0, 16, 0, 1], 'lmfdb_label': '21021.e5', 'torsion': [4, 4]}
  • id: 1070050
    {'degree': 16, 'field': [870787, 16727, -11644, 269371, -123308, -13734, 14291, -37838, 19216, 11267, -6766, -1332, 853, 74, -46, -2, 1], 'lmfdb_label': '21021.e5', 'torsion': [16]}
  • id: 1070051
    {'degree': 16, 'field': [2960857, -5988494, 7969205, -6613592, 2873829, -357740, -123798, -42716, 81091, -34798, 7032, -4, -432, 116, -4, -4, 1], 'lmfdb_label': '21021.e5', 'torsion': [16]}
  • id: 1070053
    {'degree': 16, 'field': [6610041, 0, -70746111, 0, 165909943, 0, 70464798, 0, 3622935, 0, 4626, 0, -4434, 0, 0, 0, 1], 'lmfdb_label': '21021.e5', 'torsion': [12]}
  • id: 1070049
    {'degree': 16, 'field': [10484644, 0, 99675816, 0, 257680993, 0, -102613356, 0, 13950672, 0, -764154, 0, 19420, 0, -228, 0, 1], 'lmfdb_label': '21021.e5', 'torsion': [2, 8]}
  • id: 1070052
    {'degree': 16, 'field': [60913695249, -157709673, 18437383539, -396597222, 1683814311, -166037544, 49538673, -10557549, 3179984, -333056, 170156, -8488, 3982, -259, 79, -4, 1], 'lmfdb_label': '21021.e5', '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: 477904
    {'conductor': 21021, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '21021.e5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 477905
    {'conductor': 21021, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21021.e5', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 477906
    {'conductor': 21021, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21021.e5', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 477907
    {'conductor': 21021, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21021.e5', '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: 1804529
    {'adelic_gens': [[1072, 27461, 11571, 13714], [34952, 34321, 29407, 20602], [1, 16, 0, 1], [12881, 20608, 11354, 19167], [1, 0, 16, 1], [15, 2, 47950, 48035], [5, 4, 48044, 48045], [48033, 16, 48032, 17], [1, 20608, 22316, 8709], [32033, 20608, 2296, 20721], [20591, 0, 0, 48047]], 'adelic_image': '48048.192.1.?', 'conductor': 21021, 'lmfdb_label': '21021.e5', 'prime': 0}
  • id: 97531
    {'conductor': 21021, 'elladic_image': '8.12.0.5', 'lmfdb_label': '21021.e5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 21021.e does not appear in ec_padic