Elliptic curve data - 226800.fc2

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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': '226800r', 'Clabel': '226800r2', 'Cnumber': 2, 'abc_quality': 0.977279040933613, 'absD': 2223057856320000000000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 120, 'ainvs': [0, 0, 0, 2818125, -1352868750], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 226800, 'degree': 8398080, 'elladic_images': ['8.2.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7834772173330412626215933419', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 132, 'isogeny_degrees': [1, 3], 'jinv': [1047929175, 941192], 'lmfdb_iso': '226800.fc', 'lmfdb_label': '226800.fc2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 783, -6459], 'min_quad_twist_disc': 60, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '8.2.0.a.1', '24.8.0.a.1', '60.8.0-3.a.1.1', '120.16.0.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2025], [3, 4, 40], [5, 2, 9072], [7, 8, 32400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.16637846414541243512564258802', 'prec': 107}, 'szpiro_ratio': 4.55474799969589, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, 1, 0, 0, 0, -3, 0, -2, 0, 0, 0, 3, 0, 4, 0], 'aplist': [0, 0, 0, 1, -3, -2, 3, 4, -6, 0, 4, -2, -6, 5, 6, -6, 3, -10, -4, 12, 10, 10, -3, 15, 1], 'class_deg': 3, 'class_size': 2, 'conductor': 226800, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '226800.fc', 'trace_hash': 1911896576927205947}
• 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': '0.0038221031896522302321183731302', 'prec': 110}, 'conductor': 226800, 'gens': [], 'heights': [], 'lmfdb_label': '226800.fc2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.080209853380032731240832866450', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9250364811207855497799887948069026983', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 226800.fc2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9846262
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '226800.fc2', 'torsion': [3]}
  • id: 9846263
    {'degree': 3, 'field': [-10, 15, 0, 1], 'lmfdb_label': '226800.fc2', 'torsion': [2]}
  • id: 9846265
    {'degree': 6, 'field': [405, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '226800.fc2', 'torsion': [3]}
  • id: 9846264
    {'degree': 6, 'field': [438, -180, 237, -20, 36, 0, 1], 'lmfdb_label': '226800.fc2', 'torsion': [2, 2]}
  • id: 9846266
    {'degree': 6, 'field': [8040, 2520, 90, -180, -30, 0, 1], 'lmfdb_label': '226800.fc2', 'torsion': [6]}
  • id: 9846267
    {'degree': 12, 'field': [-162936, -190620, -2538, 172080, 2610, -12060, -10710, 360, 810, -90, -63, 0, 1], 'lmfdb_label': '226800.fc2', 'torsion': [4]}
  • id: 9846268
    {'degree': 12, 'field': [196, 84, 246, -650, 315, -36, 111, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '226800.fc2', 'torsion': [3, 3]}
  • id: 9846269
    {'degree': 12, 'field': [67600, 0, -75600, 0, 58500, 0, 280, 0, 540, 0, 0, 0, 1], 'lmfdb_label': '226800.fc2', 'torsion': [2, 6]}
  • id: 9846270
    {'degree': 18, 'field': [-9720375, 0, 17695125, 0, -3701250, 0, -1464000, 0, 192375, 0, 105750, 0, 21540, 0, 1485, 0, -90, 0, 1], 'lmfdb_label': '226800.fc2', 'torsion': [9]}
  • id: 9846271
    {'degree': 18, 'field': [13824, 0, 0, -6912, 0, 0, 51480, 0, 0, 5840, 0, 0, 300, 0, 0, -12, 0, 0, 1], 'lmfdb_label': '226800.fc2', 'torsion': [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: 5623017
    {'conductor': 226800, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '226800.fc2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5623018
    {'conductor': 226800, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '226800.fc2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5623019
    {'conductor': 226800, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '226800.fc2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5623020
    {'conductor': 226800, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '226800.fc2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 3110463
    {'adelic_gens': [[4, 3, 9, 7], [114, 95, 95, 69], [89, 90, 75, 29], [1, 6, 0, 1], [23, 0, 0, 119], [1, 0, 6, 1], [115, 6, 114, 7], [61, 30, 15, 91], [3, 4, 8, 11]], 'adelic_image': '120.16.0.?', 'conductor': 226800, 'lmfdb_label': '226800.fc2', 'prime': 0}
  • id: 828560
    {'conductor': 226800, 'elladic_image': '8.2.0.1', 'lmfdb_label': '226800.fc2', 'modell_image': '2G', 'prime': 2}
  • id: 828561
    {'conductor': 226800, 'elladic_image': '3.4.0.1', 'lmfdb_label': '226800.fc2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 226800.fc does not appear in ec_padic