Elliptic curve data - 21021.e3

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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': '21021b', 'Clabel': '21021b3', 'Cnumber': 3, 'abc_quality': 0.9574733148525506, 'absD': 442766647764441, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 24024, 'ainvs': [1, 1, 1, -23227, -921544], 'analytic_rank': 0, 'bad_primes': [3, 7, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21021, 'degree': 98304, 'elladic_images': ['4.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5140507134345714739224339869', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [11779205551777, 3763454409], 'lmfdb_iso': '21021.e', 'lmfdb_label': '21021.e3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -474, 2619], 'min_quad_twist_disc': -7, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '12.24.0.c.1', '28.24.0-4.b.1.1', '84.48.0.?', '88.24.0.?', '104.24.0.?', '264.48.0.?', '312.48.0.?', '616.48.0.?', '728.48.0.?', '1144.48.0.?', '1848.96.0.?', '2184.96.0.?', '3432.96.1.?', '8008.96.0.?', '24024.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 7007], [7, 26, 429], [11, 12, 1911], [13, 14, 1617]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.54109563890691482136975761518', 'prec': 103}, 'szpiro_ratio': 4.196890816451282, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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': '0.048407456032338618316106029951', 'prec': 107}, 'conductor': 21021, 'gens': [], 'heights': [], 'lmfdb_label': '21021.e3', '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': 32, 'torsion_generators': [[-127, 63, 1], [-43, 21, 1]], 'xcoord_integral_points': [-127, -43]}
• 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.e3'}
• ec_torsion_growth •

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

  
  
  • id: 1070065
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '21021.e3', 'torsion': [2, 4]}
  • id: 1070066
    {'degree': 4, 'field': [4, -2, -1, -1, 1], 'lmfdb_label': '21021.e3', 'torsion': [2, 4]}
  • id: 1070067
    {'degree': 4, 'field': [22, 2, -1, -2, 1], 'lmfdb_label': '21021.e3', 'torsion': [2, 4]}
  • id: 1070068
    {'degree': 8, 'field': [16, 0, 12, 0, 5, 0, 3, 0, 1], 'lmfdb_label': '21021.e3', 'torsion': [4, 4]}
  • id: 1070071
    {'degree': 8, 'field': [3047, -12296, 12278, 35, -14, -7, 7, -4, 1], 'lmfdb_label': '21021.e3', 'torsion': [2, 6]}
  • id: 1070069
    {'degree': 8, 'field': [32041, 0, 10288, 0, 614, 0, -32, 0, 1], 'lmfdb_label': '21021.e3', 'torsion': [2, 8]}
  • id: 1070070
    {'degree': 8, 'field': [198916, 0, -67432, 0, 6504, 0, -172, 0, 1], 'lmfdb_label': '21021.e3', 'torsion': [2, 8]}
  • id: 1070074
    {'degree': 16, 'field': [5041, 0, 3892, 0, -3128, 0, -4137, 0, 2328, 0, -231, 0, 85, 0, -14, 0, 1], 'lmfdb_label': '21021.e3', 'torsion': [2, 12]}
  • id: 1070072
    {'degree': 16, 'field': [21904, 0, 64368, 0, 86956, 0, 63192, 0, 26409, 0, 6360, 0, 826, 0, 48, 0, 1], 'lmfdb_label': '21021.e3', 'torsion': [2, 8]}
  • id: 1070073
    {'degree': 16, 'field': [573049, 0, 58056, 0, -70334, 0, -43812, 0, 15507, 0, -1044, 0, 142, 0, -12, 0, 1], 'lmfdb_label': '21021.e3', 'torsion': [2, 8]}
• 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: 477912
    {'conductor': 21021, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21021.e3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 477913
    {'conductor': 21021, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21021.e3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 477914
    {'conductor': 21021, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '21021.e3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 477915
    {'conductor': 21021, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '21021.e3', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1804527
    {'adelic_gens': [[12937, 17164, 0, 1], [20591, 0, 0, 24023], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4298, 0, 6007], [21743, 13734, 10290, 10291], [24017, 8, 24016, 9], [5153, 14588, 4312, 22317], [5, 4, 24020, 24021], [4369, 10304, 10612, 17193]], 'adelic_image': '24024.192.1.?', 'conductor': 21021, 'lmfdb_label': '21021.e3', 'prime': 0}
  • id: 97529
    {'conductor': 21021, 'elladic_image': '4.12.0.3', 'lmfdb_label': '21021.e3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 21021.e does not appear in ec_padic