Elliptic curve data - 53550.cs6

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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
  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': '53550dt', 'Clabel': '53550dt3', 'Cnumber': 3, 'abc_quality': 1.06742381122777, 'absD': 33360312392474280633000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 4080, 'ainvs': [1, -1, 1, 78731095, -70187170903], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 53550, 'degree': 15728640, 'elladic_images': ['16.48.0.120'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5865804795941501408241933455', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 70, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4738217997934888496063, 2928751705237796928], 'lmfdb_iso': '53550.cs', 'lmfdb_label': '53550.cs6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 349916, 20936165], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '16.48.0.z.2', '60.12.0-4.c.1.2', '68.12.0.h.1', '120.48.0.?', '136.48.0.?', '240.96.0.?', '272.96.1.?', '1020.24.0.?', '2040.96.0.?', '4080.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3825], [3, 8, 2975], [5, 14, 2142], [7, 8, 7650], [17, 18, 3150]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2325553790430451078261910604', 'prec': 100}, 'szpiro_ratio': 6.076046528326425, '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, 0, 1, 0, 0, -1, 1, 0, 0, -4, 0, 2, -1, 0, 1, 1, 0, 4, 0], 'aplist': [1, 0, 0, -1, -4, 2, 1, 4, 8, -6, 0, 2, -10, 4, 0, 6, 4, 6, 12, 8, 6, 0, -12, 6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 53550, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '53550.cs', 'trace_hash': 113699391422199376}
• 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': '0.00076689477283137160239613832110', 'prec': 113}, 'conductor': 53550, 'gens': [], 'heights': [], 'lmfdb_label': '53550.cs6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.037862503892734914405344665116', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6348003737025517829130878511488886284', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[3531, -3535, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 1], '3': 'a', '5': 'a', '7': [0, 0], '17': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '53550.cs6'}
• ec_torsion_growth •

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

  
  
  • id: 2592893
    {'degree': 2, 'field': [-255, 0, 1], 'lmfdb_label': '53550.cs6', 'torsion': [4]}
  • id: 2592894
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '53550.cs6', 'torsion': [4]}
  • id: 2592892
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '53550.cs6', 'torsion': [2, 2]}
  • id: 2592897
    {'degree': 4, 'field': [34, -4, 5, -2, 1], 'lmfdb_label': '53550.cs6', 'torsion': [8]}
  • id: 2592895
    {'degree': 4, 'field': [186, -42, 43, -2, 1], 'lmfdb_label': '53550.cs6', 'torsion': [2, 4]}
  • id: 2592896
    {'degree': 4, 'field': [934, -76, 77, -2, 1], 'lmfdb_label': '53550.cs6', 'torsion': [8]}
  • id: 2592902
    {'degree': 8, 'field': [-78744, 80801, -14144, -8043, 2761, -43, -39, -4, 1], 'lmfdb_label': '53550.cs6', 'torsion': [6]}
  • id: 2592898
    {'degree': 8, 'field': [336, -24, 106, -150, 41, 38, -8, -4, 1], 'lmfdb_label': '53550.cs6', 'torsion': [2, 4]}
  • id: 2592900
    {'degree': 8, 'field': [1426, -948, 1606, -1364, 803, -148, 54, -4, 1], 'lmfdb_label': '53550.cs6', 'torsion': [2, 8]}
  • id: 2592901
    {'degree': 8, 'field': [2866, -1528, 1692, -360, 261, -100, 38, -4, 1], 'lmfdb_label': '53550.cs6', 'torsion': [16]}
  • id: 2592899
    {'degree': 8, 'field': [24649, 0, -25740, 0, 1214, 0, -60, 0, 1], 'lmfdb_label': '53550.cs6', 'torsion': [8]}
  • id: 2592910
    {'degree': 16, 'field': [82944, 0, 364272, 0, -8564, 0, -13017, 0, 2250, 0, 2759, 0, 429, 0, 30, 0, 1], 'lmfdb_label': '53550.cs6', 'torsion': [12]}
  • id: 2592903
    {'degree': 16, 'field': [112896, 0, -70656, 0, 31588, 0, 17360, 0, 11865, 0, 3088, 0, 450, 0, 32, 0, 1], 'lmfdb_label': '53550.cs6', 'torsion': [4, 4]}
  • id: 2592904
    {'degree': 16, 'field': [695556, 0, 845880, 0, 701200, 0, 117908, 0, -6987, 0, -2240, 0, 426, 0, -28, 0, 1], 'lmfdb_label': '53550.cs6', 'torsion': [2, 8]}
  • id: 2592907
    {'degree': 16, 'field': [2071714, -352616, 503396, -216200, -113374, 286848, -125752, 14520, 13555, -16392, 8576, -3368, 986, -224, 52, -8, 1], 'lmfdb_label': '53550.cs6', 'torsion': [2, 16]}
  • id: 2592905
    {'degree': 16, 'field': [34020756, -88082928, 63120864, -12403416, 2781424, 8089752, -947048, -137924, 188349, 21348, 3832, -420, -158, 140, 0, -8, 1], 'lmfdb_label': '53550.cs6', 'torsion': [2, 8]}
  • id: 2592906
    {'degree': 16, 'field': [210156976, 28848896, 28676288, -119846496, 72097102, -15117536, 5874288, -695584, 162059, -13280, 24304, -12432, 2618, -280, 60, -8, 1], 'lmfdb_label': '53550.cs6', 'torsion': [16]}
  • id: 2592909
    {'degree': 16, 'field': [614176047744, 806975045184, -851361588656, 131908853152, 40417515376, -8339674528, 215834708, 96245792, -32812876, -5919820, -345487, 140962, 11482, -608, -62, -8, 1], 'lmfdb_label': '53550.cs6', 'torsion': [12]}
  • id: 2592908
    {'degree': 16, 'field': [1582223448834, 557381704614, 220575597153, 21235379304, 2953751946, -986075988, 24443523, -10505980, 5512655, -1386668, -56385, -38320, 6229, -30, 74, -8, 1], 'lmfdb_label': '53550.cs6', 'torsion': [2, 6]}
• 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: 1285543
    {'conductor': 53550, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '53550.cs6', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 1285544
    {'conductor': 53550, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '53550.cs6', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1285545
    {'conductor': 53550, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '53550.cs6', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1285546
    {'conductor': 53550, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '53550.cs6', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1285547
    {'conductor': 53550, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '53550.cs6', 'prime': 17, '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: 2019933
    {'adelic_gens': [[4065, 16, 4064, 17], [5, 4, 4076, 4077], [1, 16, 0, 1], [2626, 2115, 1215, 1246], [2461, 1920, 60, 121], [2719, 0, 0, 4079], [15, 2, 3982, 4067], [1, 0, 16, 1], [3263, 0, 0, 4079], [3856, 1365, 1395, 4066]], 'adelic_image': '4080.192.1.?', 'conductor': 53550, 'lmfdb_label': '53550.cs6', 'prime': 0}
  • id: 228735
    {'conductor': 53550, 'elladic_image': '16.48.0.120', 'lmfdb_label': '53550.cs6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 53550.cs does not appear in ec_padic