Elliptic curve data - 221760.cv1

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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': '221760ls', 'Clabel': '221760ls4', 'Cnumber': 4, 'abc_quality': 0.9435840641150427, 'absD': 25866086400000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [0, 0, 0, -1071948, -427107728], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 221760, 'degree': 2097152, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1504289710837669948184378414', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 73, 'isogeny_degrees': [1, 2, 4], 'jinv': [1425631925916578, 270703125], 'lmfdb_iso': '221760.cv', 'lmfdb_label': '221760.cv1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -29776, 1987276], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.6', '56.12.0.z.1', '88.12.0.?', '132.12.0.?', '168.24.0.?', '264.24.0.?', '616.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.2976913531109419540155121632', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.61916432095645629411306971754', 'prec': 103}, 'szpiro_ratio': 4.327487890332542, '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, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, -1, -1, 1, 2, 2, 0, 0, -2, -4, -6, -6, -12, -4, 6, -4, 10, 4, -8, -2, 0, -16, 6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 221760, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '221760.cv', 'trace_hash': 1410741003057231822}
• 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': '0.013556922965512990050254169971', 'prec': 107}, 'conductor': 221760, 'gens': [[9396, 905000, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.2976913531109419540155121632', 'prec': 100}], 'lmfdb_label': '221760.cv1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14837511671847774523976303408', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.2883645828504504932452571633074326788', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-604, 0, 1]], 'xcoord_integral_points': [-604, 9396]}
• lmfdb_label 221760.cv1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9652460
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [2, 2]}
  • id: 9652462
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [4]}
  • id: 9652461
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [4]}
  • id: 9652463
    {'degree': 4, 'field': [2401, 0, -56, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [2, 4]}
  • id: 9652467
    {'degree': 8, 'field': [-395307, 0, 0, 0, 2178, 0, 38, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [6]}
  • id: 9652465
    {'degree': 8, 'field': [36, -72, 198, -192, 202, -52, 23, -2, 1], 'lmfdb_label': '221760.cv1', 'torsion': [8]}
  • id: 9652464
    {'degree': 8, 'field': [3018, 17448, -17372, -120, -19, 92, -26, -4, 1], 'lmfdb_label': '221760.cv1', 'torsion': [2, 4]}
  • id: 9652466
    {'degree': 8, 'field': [515524, 0, 61936, 0, 7212, 0, -152, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [8]}
  • id: 9652469
    {'degree': 16, 'field': [2643876, 0, 2980392, 0, 1159648, 0, 173516, 0, 33285, 0, 3472, 0, 714, 0, 44, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [2, 8]}
  • id: 9652468
    {'degree': 16, 'field': [9108324, 0, 409290096, 0, 305859220, 0, 2721632, 0, 1071405, 0, 43180, 0, 1374, 0, 68, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [4, 4]}
  • id: 9652470
    {'degree': 16, 'field': [413227584, 0, -787100160, 0, 337690672, 0, 109504032, 0, 16786209, 0, 734228, 0, 13200, 0, 132, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [2, 8]}
  • id: 9652472
    {'degree': 16, 'field': [5955980625, 0, 1134472500, 0, 54022500, 0, 163104732, 0, 8229942, 0, 59388, 0, 1764, 0, 84, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [12]}
  • id: 9652471
    {'degree': 16, 'field': [292213762624, 0, -2433614876672, 0, 162943768960, 0, -6285472256, 0, 170868880, 0, -3330824, 0, 40180, 0, -308, 0, 1], 'lmfdb_label': '221760.cv1', 'torsion': [2, 6]}
  • id: 9652473
    {'degree': 16, 'field': [3228669922500, 0, 587030895000, 0, -80761220100, 0, 82798848, 0, 59955984, 0, 2921292, 0, 48832, 0, 340, 0, 1], 'lmfdb_label': '221760.cv1', '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: 5500490
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '221760.cv1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 5500491
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '221760.cv1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5500492
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '221760.cv1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5500493
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.cv1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5500494
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.cv1', 'prime': 11, '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: 3079469
    {'adelic_gens': [[1072, 3, 285, 1234], [1, 0, 8, 1], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [7, 6, 1842, 1843], [1231, 0, 0, 1847], [1616, 69, 1767, 506], [796, 1233, 111, 622], [235, 1464, 1794, 853]], 'adelic_image': '1848.48.0.?', 'conductor': 221760, 'lmfdb_label': '221760.cv1', 'prime': 0}
  • id: 812339
    {'conductor': 221760, 'elladic_image': '4.6.0.1', 'lmfdb_label': '221760.cv1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 221760.cv does not appear in ec_padic