Elliptic curve data - 221760.nf2

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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': '221760hv', 'Clabel': '221760hv3', 'Cnumber': 3, 'abc_quality': 0.9670732682705956, 'absD': 8962598937600000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1848, 'ainvs': [0, 0, 0, -4620972, 3820671664], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 221760, 'degree': 6291456, 'elladic_images': ['8.24.0.26'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5653933112723895691817164983', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 343, 'isogeny_degrees': [1, 2, 4], 'jinv': [228410605013945764, 187597265625], 'lmfdb_iso': '221760.nf', 'lmfdb_label': '221760.nf2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -128360, -17645508], 'min_quad_twist_disc': -24, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0-4.b.1.4', '24.48.0-24.m.1.13', '56.48.0-56.h.2.11', '88.48.0.?', '168.96.0.?', '264.96.0.?', '616.96.0.?', '924.24.0.?', '1848.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 13, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.1929573594123288780720932627', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0918909261917409775944510512', 'prec': 100}, 'szpiro_ratio': 4.68358973172807, '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, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, 1, 1, 1, 2, -2, -4, 0, -2, -8, 10, 6, 4, 0, -2, -12, -14, -12, 0, -6, -16, -4, 14, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 221760, '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': '221760.nf', 'trace_hash': 15259661978084720}
• 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': '0.0059119082038557661222481867210', 'prec': 110}, 'conductor': 221760, 'gens': [[-82, 64800, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.1929573594123288780720932627', 'prec': 100}], 'lmfdb_label': '221760.nf2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.22964132297259611628376067832', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.7664738004909453221060418237523177651', 'prec': 130}, 'tamagawa_product': 512, 'torsion_generators': [[1214, 0, 1], [1268, 0, 1]], 'xcoord_integral_points': [-2482, -82, 1118, 1214, 1268, 1368, 2564, 3293]}
• lmfdb_label 221760.nf2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9648267
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '221760.nf2', 'torsion': [2, 4]}
  • id: 9648268
    {'degree': 4, 'field': [1369, 0, 80, 0, 1], 'lmfdb_label': '221760.nf2', 'torsion': [2, 4]}
  • id: 9648269
    {'degree': 4, 'field': [1600, 0, -74, 0, 1], 'lmfdb_label': '221760.nf2', 'torsion': [2, 4]}
  • id: 9648273
    {'degree': 8, 'field': [-59643, 0, -3282, 0, -846, 0, 0, 0, 1], 'lmfdb_label': '221760.nf2', 'torsion': [2, 6]}
  • id: 9648271
    {'degree': 8, 'field': [9, -30, 67, -98, 98, -2, -7, -2, 1], 'lmfdb_label': '221760.nf2', 'torsion': [2, 8]}
  • id: 9648272
    {'degree': 8, 'field': [9, 0, -120, 0, 79, 0, -16, 0, 1], 'lmfdb_label': '221760.nf2', 'torsion': [2, 8]}
  • id: 9648270
    {'degree': 8, 'field': [160000, 0, 0, 0, 569, 0, 0, 0, 1], 'lmfdb_label': '221760.nf2', 'torsion': [4, 4]}
  • id: 9648276
    {'degree': 16, 'field': [31640625, 0, -42187500, 0, 14062500, 0, 329724, 0, -143658, 0, -7716, 0, 36, 0, -12, 0, 1], 'lmfdb_label': '221760.nf2', 'torsion': [2, 12]}
  • id: 9648274
    {'degree': 16, 'field': [436016161, 0, 549171616, 0, 195344492, 0, 8145312, 0, -599290, 0, -1824, 0, 1196, 0, -32, 0, 1], 'lmfdb_label': '221760.nf2', 'torsion': [2, 8]}
  • id: 9648275
    {'degree': 16, 'field': [160821050625, 0, -9895171344, 0, 267912484, 0, 25214672, 0, 4057158, 0, -11312, 0, -2268, 0, -16, 0, 1], 'lmfdb_label': '221760.nf2', '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: 5498790
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '221760.nf2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 5498791
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '221760.nf2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5498792
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '221760.nf2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 5498793
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221760.nf2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5498794
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221760.nf2', 'prime': 11, '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: 3080290
    {'adelic_gens': [[1841, 8, 1840, 9], [1231, 1840, 1228, 1815], [1, 0, 8, 1], [5, 4, 1844, 1845], [1015, 2, 822, 1843], [1845, 1378, 1394, 21], [7, 6, 1578, 1843], [7, 1388, 1830, 457], [1, 8, 0, 1]], 'adelic_image': '1848.192.1.?', 'conductor': 221760, 'lmfdb_label': '221760.nf2', 'prime': 0}
  • id: 813220
    {'conductor': 221760, 'elladic_image': '8.24.0.26', 'lmfdb_label': '221760.nf2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 221760.nf does not appear in ec_padic