Elliptic curve data - 127050.eg4

Formats: - HTML - YAML - JSON - 2024-05-17T15:55:42.421402

• 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': '127050dk', 'Clabel': '127050dk1', 'Cnumber': 1, 'abc_quality': 0.8499917728489924, 'absD': 102307647750000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9240, 'ainvs': [1, 0, 1, 10524, 254098], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 127050, 'degree': 491520, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3761800074850798345022537309', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 110, 'isogeny_degrees': [1, 2, 4], 'jinv': [4657463, 3696], 'lmfdb_iso': '127050.eg', 'lmfdb_label': '127050.eg4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 4, 0], 'min_quad_twist_disc': -55, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '20.12.0-4.c.1.2', '88.12.0.?', '168.12.0.?', '440.24.0.?', '462.6.0.?', '840.24.0.?', '924.12.0.?', '1848.24.0.?', '4620.24.0.?', '9240.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.62748658513115562482909772470', 'prec': 107}, 'szpiro_ratio': 3.3523531480349718, '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, 1, 1, 0, -1, 1, -1, 1, 0, 0, 1, 2, -1, 0, 1, -6, -1, 4, 0], 'aplist': [-1, 1, 0, 1, 0, 2, -6, 4, 4, -2, -4, 2, 6, 0, 8, 14, 12, 14, -4, 12, 6, 0, 0, -6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 127050, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '127050.eg', 'trace_hash': 475453950579891777}
• 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': '0.063777168385848456903624617184', 'prec': 107}, 'conductor': 127050, 'gens': [], 'heights': [], 'lmfdb_label': '127050.eg4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.38433646542744039484360691260', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0746917234195231587488553008013364463', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-23, 11, 1]], 'xcoord_integral_points': [-23]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [5, 0], '5': 'a', '7': [1, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '127050.eg4'}
• ec_torsion_growth •

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

  
  
  • id: 5783053
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '127050.eg4', 'torsion': [4]}
  • id: 5783052
    {'degree': 2, 'field': [58, -1, 1], 'lmfdb_label': '127050.eg4', 'torsion': [2, 2]}
  • id: 5783054
    {'degree': 2, 'field': [289, -1, 1], 'lmfdb_label': '127050.eg4', 'torsion': [4]}
  • id: 5783055
    {'degree': 4, 'field': [3481, 0, 113, 0, 1], 'lmfdb_label': '127050.eg4', 'torsion': [2, 4]}
  • id: 5783059
    {'degree': 8, 'field': [-106911, -65520, -26124, -6960, -1290, -160, -12, 0, 1], 'lmfdb_label': '127050.eg4', 'torsion': [6]}
  • id: 5783057
    {'degree': 8, 'field': [-549, 4668, 4732, 2368, 633, -36, -42, -4, 1], 'lmfdb_label': '127050.eg4', 'torsion': [8]}
  • id: 5783058
    {'degree': 8, 'field': [53824, -38976, 14864, 13104, 2148, -168, -46, 0, 1], 'lmfdb_label': '127050.eg4', 'torsion': [8]}
  • id: 5783056
    {'degree': 8, 'field': [76344, 130296, 112668, 13128, 8938, -2, 195, -2, 1], 'lmfdb_label': '127050.eg4', 'torsion': [2, 4]}
  • id: 5783064
    {'degree': 16, 'field': [-424399, -415364, 109756, 254504, 100094, -76572, 5464, 16112, 15983, -2052, 2216, -392, -162, 112, -4, -8, 1], 'lmfdb_label': '127050.eg4', 'torsion': [12]}
  • id: 5783061
    {'degree': 16, 'field': [271111, -915456, 2089982, -1395328, -1445638, 1921404, 372806, -732144, 24979, 86532, 694, -8768, 612, 364, -32, -8, 1], 'lmfdb_label': '127050.eg4', 'torsion': [2, 8]}
  • id: 5783062
    {'degree': 16, 'field': [467811, -824256, 1425042, -892368, -258038, 654084, 96066, -262864, 62339, -4708, 7634, -3328, 312, 84, 8, -8, 1], 'lmfdb_label': '127050.eg4', 'torsion': [2, 8]}
  • id: 5783065
    {'degree': 16, 'field': [14677807104, 0, 1876005888, 0, 410281216, 0, -5215488, 0, 1433280, 0, 21856, 0, -1776, 0, 0, 0, 1], 'lmfdb_label': '127050.eg4', 'torsion': [12]}
  • id: 5783063
    {'degree': 16, 'field': [22120376481, -10962943488, 42433637652, -23047705800, 11211301248, -3793080312, 1038038544, -210643728, 34779822, -3979824, 304948, -21672, 6384, -856, -24, 0, 1], 'lmfdb_label': '127050.eg4', 'torsion': [2, 6]}
  • id: 5783060
    {'degree': 16, 'field': [25058573401, 0, -17700350808, 0, 3162066142, 0, -163769088, 0, 61355223, 0, -2591904, 0, 43558, 0, -336, 0, 1], 'lmfdb_label': '127050.eg4', 'torsion': [4, 4]}
• 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: 3130894
    {'conductor': 127050, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '127050.eg4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3130895
    {'conductor': 127050, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '127050.eg4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3130896
    {'conductor': 127050, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '127050.eg4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 3130897
    {'conductor': 127050, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '127050.eg4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3130898
    {'conductor': 127050, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '127050.eg4', 'prime': 11, '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: 2492111
    {'adelic_gens': [[5543, 0, 0, 9239], [6241, 6240, 1630, 2551], [4316, 5545, 1255, 6], [9233, 8, 9232, 9], [1, 0, 8, 1], [1, 8, 0, 1], [5704, 1845, 5875, 3694], [1, 4, 4, 17], [796, 5545, 8735, 6], [7, 6, 9234, 9235], [3011, 8550, 8090, 9011]], 'adelic_image': '9240.48.0.?', 'conductor': 127050, 'lmfdb_label': '127050.eg4', 'prime': 0}
  • id: 495920
    {'conductor': 127050, 'elladic_image': '4.6.0.1', 'lmfdb_label': '127050.eg4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 127050.eg does not appear in ec_padic