Elliptic curve data - 377520.ex4

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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': '377520ex', 'Clabel': '377520ex1', 'Cnumber': 1, 'abc_quality': 1.033291831982854, 'absD': 2153584375068475108990176460800, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [0, 1, 0, -3387164656, 27783206303444], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 377520, 'degree': 486604800, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.5131581531432682274490867972', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 127, 'isogeny_degrees': [1, 2, 4], 'jinv': [592265697637387401314569, 296787655248366796800], 'lmfdb_iso': '377520.ex', 'lmfdb_label': '377520.ex4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -1749568, 325439488], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '24.24.0-24.bb.1.5', '66.6.0.a.1', '88.24.0.?', '132.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '49.845254704807016692396666839', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 363], [3, 4, 125840], [5, 6, 75504], [11, 72, 3120], [13, 14, 29040]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.6210633361841376460008828868', 'prec': 100}, 'szpiro_ratio': 6.030768280501515, '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, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, -6, 0, 0, 0], 'aplist': [0, 1, -1, 0, 0, 1, -6, 0, 4, -2, 0, 6, 10, 8, -12, -6, 12, 6, -4, -4, -10, 0, 4, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 377520, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '377520.ex', 'trace_hash': 1006876485570513924}
• 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': '0.00012020447507841309990029060079', 'prec': 113}, 'conductor': 377520, 'gens': [[-3310765999339227940535, 973226352776150434031049345114853, 485142504]], 'heights': [{'__RealLiteral__': 0, 'data': '49.845254704807016692396666839', 'prec': 100}], 'lmfdb_label': '377520.ex4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.023060074479394796653453338478', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.1954822874980296319716036433287860643', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-61934, 0, 1]], 'xcoord_integral_points': [-61934]}
• lmfdb_label 377520.ex4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 15645669
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '377520.ex4', 'torsion': [2, 2]}
  • id: 15645671
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [4]}
  • id: 15645670
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [4]}
  • id: 15645673
    {'degree': 4, 'field': [-139425, 0, 0, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [2, 4]}
  • id: 15645672
    {'degree': 4, 'field': [64, 0, 17, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [2, 4]}
  • id: 15645677
    {'degree': 8, 'field': [-702768, 0, -154396, 0, -2904, 0, 0, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [6]}
  • id: 15645676
    {'degree': 8, 'field': [576, 0, 3408, 0, 1033, 0, 78, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [8]}
  • id: 15645675
    {'degree': 8, 'field': [141288, 103008, 43812, 9660, 1873, 224, 36, -4, 1], 'lmfdb_label': '377520.ex4', 'torsion': [8]}
  • id: 15645674
    {'degree': 8, 'field': [71639296, 9005696, 566048, 26504, -16847, -1082, 2, -2, 1], 'lmfdb_label': '377520.ex4', 'torsion': [4, 4]}
  • id: 15645681
    {'degree': 16, 'field': [589824, 0, 2494464, 0, 1616896, 0, 311808, 0, -69936, 0, -30044, 0, -984, 0, 0, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [2, 6]}
  • id: 15645678
    {'degree': 16, 'field': [4596736, 0, 7902464, 0, 5515664, 0, 2008896, 0, 409064, 0, 46584, 0, 2849, 0, 86, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [2, 8]}
  • id: 15645679
    {'degree': 16, 'field': [52765696, 106577408, 107633792, 81591568, 48798713, 22151260, 8282376, 2601372, 595507, 110136, 20112, 904, 59, 220, 8, -4, 1], 'lmfdb_label': '377520.ex4', 'torsion': [2, 8]}
  • id: 15645683
    {'degree': 16, 'field': [22584078400, 0, 429568256, 0, 39548704, 0, 22442164, 0, 1453028, 0, 40468, 0, 1789, 0, 74, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [12]}
  • id: 15645680
    {'degree': 16, 'field': [797048986176, 0, -5519180299104, 0, -229290043500, 0, 2539356984, 0, 145222449, 0, -955716, 0, -43470, 0, -204, 0, 1], 'lmfdb_label': '377520.ex4', 'torsion': [2, 8]}
  • id: 15645682
    {'degree': 16, 'field': [1657446156136, -346561591448, 381773192388, -72581310592, 41769365426, -6810130182, 2669023117, -354446576, 104412798, -10880324, 2526109, -195816, 36731, -1918, 294, -8, 1], 'lmfdb_label': '377520.ex4', 'torsion': [12]}
• 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: 9341196
    {'conductor': 377520, 'conductor_valuation': 4, 'discriminant_valuation': 56, 'j_denominator_valuation': 44, 'kodaira_symbol': -52, 'lmfdb_label': '377520.ex4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9341197
    {'conductor': 377520, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '377520.ex4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 9341198
    {'conductor': 377520, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '377520.ex4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9341199
    {'conductor': 377520, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '377520.ex4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9341200
    {'conductor': 377520, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '377520.ex4', 'prime': 13, 'reduction_type': 1, '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: 4011927
    {'adelic_gens': [[107, 102, 170, 35], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 258, 259], [160, 261, 67, 262], [257, 8, 256, 9], [95, 96, 218, 89], [92, 1, 199, 6]], 'adelic_image': '264.48.0.?', 'conductor': 377520, 'lmfdb_label': '377520.ex4', 'prime': 0}
  • id: 1292816
    {'conductor': 377520, 'elladic_image': '4.12.0.8', 'lmfdb_label': '377520.ex4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 377520.ex does not appear in ec_padic