Elliptic curve data - 21675.s3

Formats: - HTML - YAML - JSON - 2025-11-07T10:35:37.299116

• 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': '21675c', 'Clabel': '21675c7', 'Cnumber': 7, 'abc_quality': 1.0594919023465201, 'absD': 81175249871972578125, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 8160, 'ainvs': [1, 1, 0, -794900, -512499375], 'analytic_rank': 1, 'bad_primes': [3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 21675, 'degree': 491520, 'elladic_images': ['16.48.0.134'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5121952367222597493987825998', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 16, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-147281603041, 215233605], 'lmfdb_iso': '21675.s', 'lmfdb_label': '21675.s3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -110, -880], 'min_quad_twist_disc': 85, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.ba.2', '16.48.0.u.2', '20.12.0.h.1', '40.48.0.bm.2', '68.12.0-4.c.1.2', '80.192.5.?', '96.96.1.?', '136.48.0.?', '272.96.0.?', '340.24.0.?', '480.384.13.?', '680.96.0.?', '1360.384.5.?', '1632.192.1.?', '8160.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '36.365732880228212410488714654', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 7225], [3, 4, 7225], [5, 18, 867], [17, 146, 75]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562425', 'prec': 103}, 'szpiro_ratio': 5.371787897006048, '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, 0, -1, 0, -3, 1, 0, 4, 1, 2, 0, 0, -1, 0, 1, 4, 0], 'aplist': [1, -1, 0, 0, 4, 2, 0, 4, 0, 2, 0, -10, -10, -4, -8, 10, -4, 2, -12, 8, 10, 0, -12, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 21675, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '21675.s', 'trace_hash': 1613917019537411626}
• 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': '0.0065755932724044973581374787709', 'prec': 110}, 'conductor': 21675, 'gens': [[409264570028551525, 223997178235413405925164425, 14142156]], 'heights': [{'__RealLiteral__': 0, 'data': '36.365732880228212410488714654', 'prec': 100}], 'lmfdb_label': '21675.s3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.075958364798853507003809523789', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5245632085880724149585475491176958986', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[4475, -4475, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 3], '3': [1, 0], '5': 'a', '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 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': '21675.s3'}
• ec_torsion_growth •

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

  
  
  • id: 1101644
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '21675.s3', 'torsion': [4]}
  • id: 1101643
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [2, 2]}
  • id: 1101645
    {'degree': 2, 'field': [85, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [4]}
  • id: 1101646
    {'degree': 4, 'field': [86, -2, 3, -2, 1], 'lmfdb_label': '21675.s3', 'torsion': [2, 4]}
  • id: 1101648
    {'degree': 4, 'field': [121, 0, 12, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [8]}
  • id: 1101647
    {'degree': 4, 'field': [1849, 0, -84, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [8]}
  • id: 1101654
    {'degree': 8, 'field': [-2031, -56949, 24905, 3663, 735, -62, -3, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [6]}
  • id: 1101650
    {'degree': 8, 'field': [36, 516, -430, -156, 39, 44, -10, -4, 1], 'lmfdb_label': '21675.s3', 'torsion': [8]}
  • id: 1101651
    {'degree': 8, 'field': [134, -172, 330, -292, 87, 68, -18, -4, 1], 'lmfdb_label': '21675.s3', 'torsion': [2, 8]}
  • id: 1101649
    {'degree': 8, 'field': [621, 740, 68, 120, 149, -20, 22, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [2, 4]}
  • id: 1101652
    {'degree': 8, 'field': [11681, -2280, -6016, 80, 1206, -40, 64, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [16]}
  • id: 1101653
    {'degree': 8, 'field': [93601, 55560, 25424, 5040, 566, -120, -16, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [16]}
  • id: 1101657
    {'degree': 16, 'field': [1021, 168052, -23974, -210732, -67304, 152396, 29934, -49316, -9603, 10324, 1794, -1564, -164, 168, -4, -8, 1], 'lmfdb_label': '21675.s3', 'torsion': [16]}
  • id: 1101660
    {'degree': 16, 'field': [1849, 0, 30079, 0, 1254055, 0, 345042, 0, 14925, 0, -2583, 0, -173, 0, 10, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [2, 6]}
  • id: 1101661
    {'degree': 16, 'field': [17161, 0, -346021, 0, 269212, 0, -118893, 0, 28185, 0, -4467, 0, 487, 0, -34, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [12]}
  • id: 1101656
    {'degree': 16, 'field': [194481, 0, -284528, 0, 178690, 0, -67888, 0, 20099, 0, -3952, 0, 470, 0, -32, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [2, 8]}
  • id: 1101655
    {'degree': 16, 'field': [276676, 0, -115704, 0, 72600, 0, 35604, 0, 19549, 0, 4464, 0, 570, 0, 36, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [4, 4]}
  • id: 1101659
    {'degree': 16, 'field': [6600326, -1711208, 1780636, -244872, 396586, -352504, 151324, -19976, -2433, -776, 5444, -2344, -34, 168, -4, -8, 1], 'lmfdb_label': '21675.s3', 'torsion': [2, 16]}
  • id: 1101658
    {'degree': 16, 'field': [88529281, 0, 0, 0, -1118592, 0, 0, 0, 24679, 0, 0, 0, -288, 0, 0, 0, 1], 'lmfdb_label': '21675.s3', 'torsion': [16]}
  • id: 1101662
    {'degree': 16, 'field': [41476173649, 0, 15680235173, 0, 2581811080, 0, 242803881, 0, 14277225, 0, 537399, 0, 12643, 0, 170, 0, 1], 'lmfdb_label': '21675.s3', '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: 494009
    {'conductor': 21675, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '21675.s3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 494010
    {'conductor': 21675, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '21675.s3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 494011
    {'conductor': 21675, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21675.s3', 'prime': 17, 'reduction_type': 0, '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: 1808973
    {'adelic_gens': [[7141, 4352, 5236, 4353], [1, 0, 32, 1], [1, 32, 0, 1], [5, 28, 68, 381], [23, 18, 5598, 6155], [5441, 4352, 3536, 4353], [8129, 32, 8128, 33], [3839, 0, 0, 8159], [6986, 2397, 595, 1172], [7260, 2431, 2159, 324]], 'adelic_image': '8160.768.13.?', 'conductor': 21675, 'lmfdb_label': '21675.s3', 'prime': 0}
  • id: 100372
    {'conductor': 21675, 'elladic_image': '16.48.0.134', 'lmfdb_label': '21675.s3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1017777
    {'lmfdb_iso': '21675.s', 'p': 11, 'prec': 20, 'unit': 13467896696423701833, 'val': 1}
  • id: 1017783
    {'lmfdb_iso': '21675.s', 'p': 13, 'prec': 20, 'unit': 873745235657083841958, 'val': 1}
  • id: 1017785
    {'lmfdb_iso': '21675.s', 'p': 19, 'prec': 20, 'unit': 1786997467081226723591126, 'val': 1}
  • id: 1017782
    {'lmfdb_iso': '21675.s', 'p': 29, 'prec': 20, 'unit': 5728926769067599811607244674, 'val': 1}
  • id: 1017778
    {'lmfdb_iso': '21675.s', 'p': 37, 'prec': 20, 'unit': 325604035163841658787664846611, 'val': 1}
  • id: 1017780
    {'lmfdb_iso': '21675.s', 'p': 41, 'prec': 20, 'unit': 2335946351013533735080934282450, 'val': 1}
  • id: 1017781
    {'lmfdb_iso': '21675.s', 'p': 43, 'prec': 20, 'unit': 6222907997924789226746005107040, 'val': 1}
  • id: 1017784
    {'lmfdb_iso': '21675.s', 'p': 47, 'prec': 20, 'unit': 39907471382506937346550816696260, 'val': 1}
  • id: 1017786
    {'lmfdb_iso': '21675.s', 'p': 53, 'prec': 20, 'unit': 424357541189451579184730685357588, 'val': 1}
  • id: 1017790
    {'lmfdb_iso': '21675.s', 'p': 59, 'prec': 20, 'unit': 4041636160611928628954239719257161, 'val': 1}
  • id: 1017791
    {'lmfdb_iso': '21675.s', 'p': 61, 'prec': 20, 'unit': 6954756822031184756905048681627252, 'val': 1}
  • id: 1017776
    {'lmfdb_iso': '21675.s', 'p': 67, 'prec': 20, 'unit': 26535405373951341072606381452439983, 'val': 1}
  • id: 1017779
    {'lmfdb_iso': '21675.s', 'p': 71, 'prec': 20, 'unit': 98198907289403568084475322386884055, 'val': 1}
  • id: 1017787
    {'lmfdb_iso': '21675.s', 'p': 73, 'prec': 20, 'unit': 244135522648859087454542542971791195, 'val': 1}
  • id: 1017788
    {'lmfdb_iso': '21675.s', 'p': 83, 'prec': 20, 'unit': 1628457727739871329910446035115591472, 'val': 1}
  • id: 1017789
    {'lmfdb_iso': '21675.s', 'p': 89, 'prec': 20, 'unit': 3487714072107669045655391167430487101, 'val': 1}
  • id: 1017775
    {'lmfdb_iso': '21675.s', 'p': 97, 'prec': 20, 'unit': 12424474223728523914088093700010610273, 'val': 1}