Elliptic curve data - 200376.k3

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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': '200376c', 'Clabel': '200376c1', 'Cnumber': 1, 'abc_quality': 1.0662343776302834, 'absD': 12832025739984, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 6072, 'ainvs': [0, 0, 0, -225786, -41294275], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 200376, 'degree': 983040, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6741776340221527627279990012', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [61604313088, 621], 'lmfdb_iso': '200376.k', 'lmfdb_label': '200376.k3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -207, -1080], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '44.12.0-4.c.1.2', '138.6.0.?', '184.12.0.?', '264.24.0.?', '276.12.0.?', '552.24.0.?', '2024.24.0.?', '3036.24.0.?', '6072.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 25047], [3, 2, 22264], [11, 62, 1656], [23, 24, 8712]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.30512520689773579147300611340', 'prec': 107}, 'szpiro_ratio': 3.9806542710776753, '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, -2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, -2, 4, 0, 2, -2, 0, -1, -2, 0, -10, -6, -8, 8, 6, 4, -14, 8, 8, 6, -12, -12, 2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 200376, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '200376.k', 'trace_hash': 942065523408775962}
• 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': '0.035142105939307780545166953534', 'prec': 107}, 'conductor': 200376, 'gens': [], 'heights': [], 'lmfdb_label': '200376.k3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.21901585978524868444204453844', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7521268782819894755363563074929963027', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-275, 0, 1]], 'xcoord_integral_points': [-275]}
• lmfdb_label 200376.k3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8781195
    {'degree': 2, 'field': [-17, -1, 1], 'lmfdb_label': '200376.k3', 'torsion': [2, 2]}
  • id: 8781197
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '200376.k3', 'torsion': [4]}
  • id: 8781196
    {'degree': 2, 'field': [190, -1, 1], 'lmfdb_label': '200376.k3', 'torsion': [4]}
  • id: 8781198
    {'degree': 4, 'field': [400, 0, -29, 0, 1], 'lmfdb_label': '200376.k3', 'torsion': [2, 4]}
  • id: 8781202
    {'degree': 8, 'field': [-5843, 6074, 1746, -602, 4, 28, -6, -4, 1], 'lmfdb_label': '200376.k3', 'torsion': [6]}
  • id: 8781199
    {'degree': 8, 'field': [2704, 0, -14432, 0, 588, 0, -44, 0, 1], 'lmfdb_label': '200376.k3', 'torsion': [2, 4]}
  • id: 8781201
    {'degree': 8, 'field': [3481, 1530, 986, 570, 171, -30, -16, 0, 1], 'lmfdb_label': '200376.k3', 'torsion': [8]}
  • id: 8781200
    {'degree': 8, 'field': [25624, -7704, 9514, -3542, 1577, 230, -72, -4, 1], 'lmfdb_label': '200376.k3', 'torsion': [8]}
  • id: 8781208
    {'degree': 16, 'field': [12981, 26382, 13082, 23942, 20150, -534, 16082, -3320, 5501, -380, 1080, 12, 178, -4, 20, 0, 1], 'lmfdb_label': '200376.k3', 'torsion': [12]}
  • id: 8781203
    {'degree': 16, 'field': [550564, 0, -609888, 0, 278596, 0, -54612, 0, 1341, 0, 900, 0, 310, 0, 24, 0, 1], 'lmfdb_label': '200376.k3', 'torsion': [4, 4]}
  • id: 8781204
    {'degree': 16, 'field': [12305232, -2782368, 4221648, -2967984, 1746204, -421176, 313428, -141204, 30541, -2972, 6244, -2468, -74, 196, -8, -8, 1], 'lmfdb_label': '200376.k3', 'torsion': [2, 8]}
  • id: 8781207
    {'degree': 16, 'field': [39963438, -32712192, 9467502, 4672698, -1915340, 2338606, 172912, -37710, 216303, -61702, 36198, -7394, 2424, -282, 76, -4, 1], 'lmfdb_label': '200376.k3', 'torsion': [12]}
  • id: 8781205
    {'degree': 16, 'field': [46512400, -18304880, -15861384, 10755272, 1581528, -1445124, -443162, -264406, 301521, 14506, -23240, -5862, 2511, 100, -48, -4, 1], 'lmfdb_label': '200376.k3', 'torsion': [2, 8]}
  • id: 8781206
    {'degree': 16, 'field': [1379156769, 0, -530385876, 0, 88833316, 0, -8775704, 0, 508082, 0, -33800, 0, 1892, 0, -68, 0, 1], 'lmfdb_label': '200376.k3', '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: 4957771
    {'conductor': 200376, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '200376.k3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4957772
    {'conductor': 200376, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '200376.k3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4957773
    {'conductor': 200376, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '200376.k3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4957774
    {'conductor': 200376, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '200376.k3', 'prime': 23, '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: 2947020
    {'adelic_gens': [[7, 6, 6066, 6067], [6065, 8, 6064, 9], [2759, 0, 0, 6071], [5908, 2761, 2783, 1662], [2936, 3861, 2387, 3310], [1, 0, 8, 1], [1, 8, 0, 1], [4489, 4488, 4774, 2839], [1, 4, 4, 17], [2971, 2970, 1738, 5875]], 'adelic_image': '6072.48.0.?', 'conductor': 200376, 'lmfdb_label': '200376.k3', 'prime': 0}
  • id: 742440
    {'conductor': 200376, 'elladic_image': '4.6.0.1', 'lmfdb_label': '200376.k3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 200376.k does not appear in ec_padic