Elliptic curve data - 378560.hr4

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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': '378560hr', 'Clabel': '378560hr1', 'Cnumber': 1, 'abc_quality': 0.895954553441358, 'absD': 2724307765962997760, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 10920, 'ainvs': [0, -1, 0, -2525761, 1543828545], 'analytic_rank': 1, 'bad_primes': [2, 5, 7, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 378560, 'degree': 9289728, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4370336610078645016403570996', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 199, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [1408317602329, 2153060], 'lmfdb_iso': '378560.hr', 'lmfdb_label': '378560.hr4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -234, 1352], 'min_quad_twist_disc': 104, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '56.6.0.d.1', '120.24.0.?', '130.6.0.?', '168.24.0.?', '312.24.0.?', '390.24.0.?', '420.24.0.?', '840.48.0.?', '1092.24.0.?', '1560.48.0.?', '2184.48.0.?', '3640.12.0.?', '5460.48.0.?', '10920.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.5052904520386799682282254409', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 845], [5, 6, 75712], [7, 8, 54080], [13, 98, 2240]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.11483821143717816948776519663', 'prec': 103}, 'szpiro_ratio': 4.347492817540079, '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, 2, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0], 'aplist': [0, 2, -1, -1, 0, 0, 0, 2, -6, -6, -8, -10, 12, 4, 0, 12, 6, -2, -4, 6, 10, -16, 0, 12, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 378560, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '378560.hr', 'trace_hash': 336002842098673835}
• 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': '0.0076422186250176611545934599814', 'prec': 110}, 'conductor': 378560, 'gens': [[369, 25728, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.5052904520386799682282254409', 'prec': 100}], 'lmfdb_label': '378560.hr4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25523374676523512717731261384', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.1992172987157770977808197020860872178', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[945, 0, 1]], 'xcoord_integral_points': [369, 945]}
• lmfdb_label 378560.hr4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 15686631
    {'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '378560.hr4', 'torsion': [6]}
  • id: 15686630
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '378560.hr4', 'torsion': [2, 2]}
  • id: 15686632
    {'degree': 4, 'field': [-31, -56, -24, 0, 1], 'lmfdb_label': '378560.hr4', 'torsion': [4]}
  • id: 15686633
    {'degree': 4, 'field': [16, 0, -18, 0, 1], 'lmfdb_label': '378560.hr4', 'torsion': [2, 6]}
  • id: 15686634
    {'degree': 6, 'field': [813903, -37878, 18823, -152, 189, -2, 1], 'lmfdb_label': '378560.hr4', 'torsion': [6]}
  • id: 15686635
    {'degree': 8, 'field': [-2974, 9660, -8094, 560, 1347, -140, -86, 0, 1], 'lmfdb_label': '378560.hr4', 'torsion': [2, 4]}
  • id: 15686637
    {'degree': 8, 'field': [-55, 580, -244, -636, 229, 104, -30, -4, 1], 'lmfdb_label': '378560.hr4', 'torsion': [12]}
  • id: 15686636
    {'degree': 8, 'field': [39256, -20024, 19990, 84, -81, 44, -10, -4, 1], 'lmfdb_label': '378560.hr4', 'torsion': [2, 4]}
  • id: 15686638
    {'degree': 12, 'field': [528529, 2705894, 12115027, 8515446, 4823694, 1545382, 372687, -19186, 13266, -282, 127, -2, 1], 'lmfdb_label': '378560.hr4', 'torsion': [3, 6]}
  • id: 15686639
    {'degree': 12, 'field': [111279496, 6526896, -6310036, -388680, 85170, 121476, -24839, -12966, 2685, 360, -61, -6, 1], 'lmfdb_label': '378560.hr4', 'torsion': [2, 6]}
  • id: 15686641
    {'degree': 16, 'field': [-871, 1976, 32452, 42536, -144346, -421392, -350344, -5744, 125263, 35824, -15440, -5872, 1010, 360, -44, -8, 1], 'lmfdb_label': '378560.hr4', 'torsion': [2, 12]}
  • id: 15686642
    {'degree': 16, 'field': [173056, 0, 173056, 0, 802880, 0, 683904, 0, 157504, 0, 464, 0, -320, 0, 16, 0, 1], 'lmfdb_label': '378560.hr4', 'torsion': [2, 12]}
  • id: 15686640
    {'degree': 16, 'field': [216217544, 463968512, -1467661184, 906578224, -1630396, -233983056, 97421244, -16041960, 2530193, -539216, -18520, 15136, 86, 448, -84, -8, 1], 'lmfdb_label': '378560.hr4', 'torsion': [8]}
  • id: 15686643
    {'degree': 18, 'field': [-46447088, -149915616, 212393424, -124461776, 30052248, 2595552, -4892252, 7639488, -3851784, 855932, -435930, 115764, 129, 1584, 720, -374, 9, -6, 1], 'lmfdb_label': '378560.hr4', 'torsion': [18]}
• 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: 9367415
    {'conductor': 378560, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '378560.hr4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 9367416
    {'conductor': 378560, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '378560.hr4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9367417
    {'conductor': 378560, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '378560.hr4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9367418
    {'conductor': 378560, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '378560.hr4', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 4018262
    {'adelic_gens': [[7801, 12, 3126, 73], [5919, 7738, 3206, 5021], [1670, 10917, 4227, 8], [10, 3, 4341, 10912], [11, 2, 10870, 10911], [1, 0, 12, 1], [7289, 2, 1878, 13], [10909, 12, 10908, 13], [1, 6, 6, 37], [1, 12, 0, 1], [5459, 10908, 10914, 10847]], 'adelic_image': '10920.96.1.?', 'conductor': 378560, 'lmfdb_label': '378560.hr4', 'prime': 0}
  • id: 1296238
    {'conductor': 378560, 'elladic_image': '2.3.0.1', 'lmfdb_label': '378560.hr4', 'modell_image': '2B', 'prime': 2}
  • id: 1296239
    {'conductor': 378560, 'elladic_image': '3.4.0.1', 'lmfdb_label': '378560.hr4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 378560.hr does not appear in ec_padic