Elliptic curve data - 2205.i1

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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': '2205j', 'Clabel': '2205j7', 'Cnumber': 7, 'abc_quality': 1.0735374703334082, 'absD': 34735279005, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [1, -1, 0, -952569, -357605172], 'analytic_rank': 0, 'bad_primes': [3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 2205, 'degree': 12288, 'elladic_images': ['16.48.0.121'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8131308273388130202239346145', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 16, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [1114544804970241, 405], 'lmfdb_iso': '2205.i', 'lmfdb_label': '2205.i1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -2160, -39540], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '10.6.0.a.1', '16.48.0.x.2', '20.12.0.g.1', '40.48.0.bj.1', '80.96.1.?', '84.12.0.?', '96.96.1.?', '160.192.5.?', '168.48.0.?', '224.96.0.?', '240.192.5.?', '336.96.0.?', '420.24.0.?', '480.384.13.?', '560.192.1.?', '672.192.1.?', '840.96.0.?', '1120.384.5.?', '1680.384.5.?', '3360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 16, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562432', 'prec': 103}, 'szpiro_ratio': 6.873348756386514, '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, 1, 0, 0, -3, 0, 1, 4, 0, 2, 0, 0, -1, 2, 0, -4, -1], 'aplist': [1, 0, 1, 0, 4, 2, 2, -4, 0, 2, 0, -10, 10, 4, 8, 10, -4, 2, 12, 8, -10, 0, 12, -6, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 2205, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '2205.i', 'trace_hash': 2170948616594710590}
• 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': '0.026615496578780108354365985501', 'prec': 107}, 'conductor': 2205, 'gens': [], 'heights': [], 'lmfdb_label': '2205.i1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15281832047796636943836082252', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4450931276474619110137731602636940431', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-2253, 2253, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 3], '3': 'a', '5': [1, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '2205.i1'}
• ec_torsion_growth •

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

  
  
  • id: 112280
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '2205.i1', 'torsion': [2, 2]}
  • id: 112282
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [4]}
  • id: 112281
    {'degree': 2, 'field': [105, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [4]}
  • id: 112284
    {'degree': 4, 'field': [121, 0, 20, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [8]}
  • id: 112283
    {'degree': 4, 'field': [505, -40, 41, -2, 1], 'lmfdb_label': '2205.i1', 'torsion': [2, 4]}
  • id: 112285
    {'degree': 4, 'field': [961, 0, 22, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [8]}
  • id: 112291
    {'degree': 8, 'field': [-243, -121, 100, -108, 112, -16, -9, -1, 1], 'lmfdb_label': '2205.i1', 'torsion': [6]}
  • id: 112286
    {'degree': 8, 'field': [295, 820, -680, -260, 81, 56, -14, -4, 1], 'lmfdb_label': '2205.i1', 'torsion': [2, 4]}
  • id: 112287
    {'degree': 8, 'field': [1005, 180, -20, -300, 101, 56, -14, -4, 1], 'lmfdb_label': '2205.i1', 'torsion': [8]}
  • id: 112288
    {'degree': 8, 'field': [23209, -5892, 6520, -1292, 737, -112, 42, -4, 1], 'lmfdb_label': '2205.i1', 'torsion': [2, 8]}
  • id: 112289
    {'degree': 8, 'field': [286225, 0, -16400, 0, -420, 0, 40, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [16]}
  • id: 112290
    {'degree': 8, 'field': [378225, 0, 20400, 0, 1420, 0, 40, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [16]}
  • id: 112293
    {'degree': 16, 'field': [25, 0, 0, 0, 0, 0, 0, 0, -2635, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [2, 8]}
  • id: 112297
    {'degree': 16, 'field': [225, 3075, 13475, 27590, 29365, 15675, 2199, -1194, 1681, 1654, 41, 375, -51, 24, 11, -1, 1], 'lmfdb_label': '2205.i1', 'torsion': [2, 6]}
  • id: 112295
    {'degree': 16, 'field': [625, 0, 0, 0, -4600, 0, 0, 0, 13239, 0, 0, 0, -184, 0, 0, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [16]}
  • id: 112299
    {'degree': 16, 'field': [531441, 0, 962373, 0, 611656, 0, 223401, 0, 53001, 0, 8119, 0, 771, 0, 42, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [12]}
  • id: 112292
    {'degree': 16, 'field': [933156, 0, -1145760, 0, 622276, 0, -207220, 0, 48861, 0, -7580, 0, 726, 0, -40, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [4, 4]}
  • id: 112294
    {'degree': 16, 'field': [1010025, 0, 72600, 0, 311410, 0, 142340, 0, 47811, 0, 8404, 0, 846, 0, 44, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [2, 8]}
  • id: 112298
    {'degree': 16, 'field': [1265625, 0, 3750000, 0, 2706250, 0, 1179375, 0, 275625, 0, 34445, 0, 2265, 0, 75, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [12]}
  • id: 112296
    {'degree': 16, 'field': [174900625, 0, 5290000, 0, 3999500, 0, 1098000, 0, 112175, 0, 4800, 0, 620, 0, 40, 0, 1], 'lmfdb_label': '2205.i1', 'torsion': [2, 16]}
• 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: 36992
    {'conductor': 2205, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '2205.i1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 36993
    {'conductor': 2205, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2205.i1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 36994
    {'conductor': 2205, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '2205.i1', 'prime': 7, 'reduction_type': 0, '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: 1678329
    {'adelic_gens': [[2057, 1414, 2058, 2869], [1, 0, 32, 1], [1, 32, 0, 1], [1439, 0, 0, 3359], [5, 28, 68, 381], [1471, 2912, 2310, 1], [421, 2912, 1876, 2913], [3329, 32, 3328, 33], [1072, 2905, 1463, 3186], [23, 18, 798, 1355]], 'adelic_image': '3360.768.13.?', 'conductor': 2205, 'lmfdb_label': '2205.i1', 'prime': 0}
  • id: 10883
    {'conductor': 2205, 'elladic_image': '16.48.0.121', 'lmfdb_label': '2205.i1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 2205.i does not appear in ec_padic