Elliptic curve data - 271440.dj1

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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': '271440dj', 'Clabel': '271440dj4', 'Cnumber': 4, 'abc_quality': 0.979301247761611, 'absD': 44522946000000000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 45240, 'ainvs': [0, 0, 0, -46951707, -123829390006], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13, 29], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 271440, 'degree': 11796480, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9832865441975835019636017039', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 87, 'isogeny_degrees': [1, 2, 4], 'jinv': [3833455222908263170009, 14910644531250], 'lmfdb_iso': '271440.dj', 'lmfdb_label': '271440.dj1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -326054, -71687698], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '120.12.0.?', '156.12.0.?', '520.12.0.?', '696.12.0.?', '1160.12.0.?', '1560.24.0.?', '3016.12.0.?', '3480.24.0.?', '9048.24.0.?', '15080.24.0.?', '45240.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7408332193035833468487469640', 'prec': 100}, 'szpiro_ratio': 5.163850216819562, '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, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, 1, 0, 0, -1, 2, 0, 0, -1, 0, 2, 2, -4, 8, 6, -12, -2, 4, 4, 6, -8, -4, -6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 271440, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '271440.dj', 'trace_hash': 631870524214440832}
• 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': '0.0025630095938524631116880337045', 'prec': 110}, 'conductor': 271440, 'gens': [], 'heights': [], 'lmfdb_label': '271440.dj1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.057674894590124186957949857096', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7683949403259609739815931406301329024', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-3962, 0, 1]], 'xcoord_integral_points': [-3962]}
• lmfdb_label 271440.dj1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11595702
    {'degree': 2, 'field': [-754, 0, 1], 'lmfdb_label': '271440.dj1', 'torsion': [2, 2]}
  • id: 11595704
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '271440.dj1', 'torsion': [4]}
  • id: 11595703
    {'degree': 2, 'field': [174, 0, 1], 'lmfdb_label': '271440.dj1', 'torsion': [4]}
  • id: 11595705
    {'degree': 4, 'field': [27070, -368, 369, -2, 1], 'lmfdb_label': '271440.dj1', 'torsion': [2, 4]}
  • id: 11595709
    {'degree': 8, 'field': [-300, 0, -2532, 0, 468, 0, -23, 0, 1], 'lmfdb_label': '271440.dj1', 'torsion': [6]}
  • id: 11595708
    {'degree': 8, 'field': [372100, 0, 19155, 0, 3491, 0, -123, 0, 1], 'lmfdb_label': '271440.dj1', 'torsion': [8]}
  • id: 11595706
    {'degree': 8, 'field': [27720225, 0, -3413124, 0, -4446, 0, -156, 0, 1], 'lmfdb_label': '271440.dj1', 'torsion': [2, 4]}
  • id: 11595707
    {'degree': 8, 'field': [1135083481, 0, -12016484, 0, 136026, 0, -524, 0, 1], 'lmfdb_label': '271440.dj1', 'torsion': [8]}
  • id: 11595715
    {'degree': 16, 'field': [10131775000, -1128105640, 1079701892, 99818216, -57427656, 8997632, -2951666, -59894, 52821, -47162, 31868, -12898, 2726, -294, 62, -8, 1], 'lmfdb_label': '271440.dj1', 'torsion': [12]}
  • id: 11595714
    {'degree': 16, 'field': [1598439318436, 0, -169598834656, 0, 16142547328, 0, -739094308, 0, 2213284, 0, 447152, 0, -3407, 0, -46, 0, 1], 'lmfdb_label': '271440.dj1', 'torsion': [12]}
  • id: 11595712
    {'degree': 16, 'field': [215546566390000, 37362593324000, -27270144888400, -3263069782800, 1711243544320, 131304455080, -60114895164, -3034361980, 1262092713, 42966872, -16282668, -372080, 126670, 1824, -544, -4, 1], 'lmfdb_label': '271440.dj1', 'torsion': [2, 8]}
  • id: 11595710
    {'degree': 16, 'field': [2022053572562500, 0, -69361428175024, 0, -509157547676, 0, 16731641072, 0, 326772253, 0, -565972, 0, -24578, 0, -76, 0, 1], 'lmfdb_label': '271440.dj1', 'torsion': [4, 4]}
  • id: 11595713
    {'degree': 16, 'field': [24512483367036900, 0, 1296208500495552, 0, 28769107366944, 0, 300655983804, 0, 682712436, 0, -12096624, 0, -79967, 0, -46, 0, 1], 'lmfdb_label': '271440.dj1', 'torsion': [2, 6]}
  • id: 11595711
    {'degree': 16, 'field': [2549890850923870756, 0, -70213352382428208, 0, 860528158853548, 0, -6403817863056, 0, 34985153445, 0, -143941236, 0, 418078, 0, -828, 0, 1], 'lmfdb_label': '271440.dj1', '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: 6727482
    {'conductor': 271440, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '271440.dj1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6727483
    {'conductor': 271440, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '271440.dj1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6727484
    {'conductor': 271440, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '271440.dj1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 6727485
    {'conductor': 271440, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '271440.dj1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6727486
    {'conductor': 271440, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '271440.dj1', 'prime': 29, '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: 3380055
    {'adelic_gens': [[41764, 15081, 44103, 30166], [1, 8, 0, 1], [45233, 8, 45232, 9], [39581, 24504, 32022, 9419], [7, 6, 45234, 45235], [1, 0, 8, 1], [18097, 30168, 42228, 30193], [5656, 13203, 32049, 1918], [43168, 3, 36405, 15082], [15079, 0, 0, 45239], [1, 4, 4, 17]], 'adelic_image': '45240.48.0.?', 'conductor': 271440, 'lmfdb_label': '271440.dj1', 'prime': 0}
  • id: 969954
    {'conductor': 271440, 'elladic_image': '4.6.0.1', 'lmfdb_label': '271440.dj1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 271440.dj does not appear in ec_padic