Elliptic curve data - 221760.dy2

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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': '221760kz', 'Clabel': '221760kz6', 'Cnumber': 6, 'abc_quality': 1.0262644607334475, 'absD': 5503824892333721124864000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, 0, 0, -931085868, 10336419100208], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 221760, 'degree': 127401984, 'elladic_images': ['2.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.0746943449388938807373490524', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 6, 'iso_nlabel': 102, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [467116778179943012100169, 28800309694464000000], 'lmfdb_iso': '221760.dy', 'lmfdb_label': '221760.dy2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1616469, -747850208], 'min_quad_twist_disc': -24, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1', '12.48.0-6.a.1.6', '24.96.0-24.o.2.26', '40.12.0.b.1', '60.96.0-60.a.1.18', '120.192.1.?', '616.12.0.?', '924.96.0.?', '1540.12.0.?', '1848.192.1.?', '3080.24.0.?', '4620.192.1.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '22.036453590229698487658327419', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4856674297649210709138782518', 'prec': 100}, 'szpiro_ratio': 5.976691155504069, '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, 6, 0, 4, 0], 'aplist': [0, 0, -1, 1, -1, -2, 6, 4, 0, -6, -4, -2, 6, 4, 0, -6, 12, -14, 16, 0, 2, -4, 0, 6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 221760, 'isogeny_matrix': [[1, 2, 3, 4, 6, 12, 12, 4], [2, 1, 6, 2, 3, 6, 6, 2], [3, 6, 1, 12, 2, 4, 4, 12], [4, 2, 12, 1, 6, 3, 12, 4], [6, 3, 2, 6, 1, 2, 2, 6], [12, 6, 4, 3, 2, 1, 4, 12], [12, 6, 4, 12, 2, 4, 1, 3], [4, 2, 12, 4, 6, 12, 3, 1]], 'lmfdb_iso': '221760.dy', 'trace_hash': 1437651106021243468}
• 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': '0.00028891192043739093306698478937', 'prec': 113}, 'conductor': 221760, 'gens': [[318826849669, 149391372309204375, 2579]], 'heights': [{'__RealLiteral__': 0, 'data': '22.036453590229698487658327419', 'prec': 100}], 'lmfdb_label': '221760.dy2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.042121135979914006858173363720', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.4256036655130347644329284023916677331', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[14134, 0, 1], [20884, 0, 1]], 'xcoord_integral_points': [-35018, 14134, 20884]}
• lmfdb_label 221760.dy2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9651771
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 6]}
  • id: 9651773
    {'degree': 4, 'field': [25, 0, 20, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 4]}
  • id: 9651774
    {'degree': 4, 'field': [11664, 0, -246, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 4]}
  • id: 9651772
    {'degree': 4, 'field': [23716, 0, 154, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 4]}
  • id: 9651775
    {'degree': 6, 'field': [1176, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 6]}
  • id: 9651777
    {'degree': 8, 'field': [36, 0, -12, 0, 13, 0, 8, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 12]}
  • id: 9651776
    {'degree': 8, 'field': [163447, 28164, -26060, -4136, 1889, 212, -66, -4, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 12]}
  • id: 9651778
    {'degree': 8, 'field': [7150276, 0, -706916, 0, 21477, 0, -254, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 12]}
  • id: 9651779
    {'degree': 12, 'field': [24025, 39060, 23028, 3024, -4314, -504, 350, -504, 24, 0, 6, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [6, 6]}
  • id: 9651781
    {'degree': 16, 'field': [65536, 0, 65536, 0, 1972736, 0, -1915392, 0, 55498148, 0, -119712, 0, 7706, 0, 16, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 8]}
  • id: 9651782
    {'degree': 16, 'field': [13549761, 0, 4183488, 0, 305928, 0, -34704, 0, 20530, 0, 8256, 0, 968, 0, 48, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 8]}
  • id: 9651780
    {'degree': 16, 'field': [11019960576, 0, 0, 0, -108440208, 0, 0, 0, 962113, 0, 0, 0, -1033, 0, 0, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [4, 4]}
  • id: 9651783
    {'degree': 16, 'field': [14821171236, 54777968208, -129002663208, 109754716464, -27754040084, -8458171672, 5031589260, -327173248, -189249531, 31551736, 1334400, -615584, 26541, 4052, -342, -4, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 8]}
  • id: 9651784
    {'degree': 18, 'field': [-3190299461432, -17255370931056, -11655838114884, -34334983680, 2360365050150, 666563252724, -71025765711, -54378716148, -3072084336, 1775150520, 221440923, -28627272, -5319186, 227268, 64215, -708, -396, 0, 1], 'lmfdb_label': '221760.dy2', 'torsion': [2, 18]}
• 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: 5500195
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 36, 'j_denominator_valuation': 18, 'kodaira_symbol': -30, 'lmfdb_label': '221760.dy2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 5500196
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '221760.dy2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5500197
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '221760.dy2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5500198
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221760.dy2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5500199
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '221760.dy2', '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: 3079564
    {'adelic_gens': [[2521, 12, 5886, 73], [9, 4, 9224, 9233], [3079, 9228, 7700, 9239], [4619, 9234, 0, 9239], [5281, 12, 3966, 73], [2311, 6, 0, 1], [1, 0, 12, 1], [9229, 12, 9228, 13], [7399, 6, 5538, 9235], [1, 12, 0, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 221760, 'lmfdb_label': '221760.dy2', 'prime': 0}
  • id: 812457
    {'conductor': 221760, 'elladic_image': '2.6.0.1', 'lmfdb_label': '221760.dy2', 'modell_image': '2Cs', 'prime': 2}
  • id: 812458
    {'conductor': 221760, 'elladic_image': '3.4.0.1', 'lmfdb_label': '221760.dy2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 221760.dy does not appear in ec_padic