Elliptic curve data - 6050.e2

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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': '6050r', 'Clabel': '6050r1', 'Cnumber': 1, 'abc_quality': 0.819897052104778, 'absD': 378125000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 264, 'ainvs': [1, 0, 1, -201, 548], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 6050, 'degree': 2880, 'elladic_images': ['8.2.0.2', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.34261045010524917605023704661', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 3], 'jinv': [18865, 8], 'lmfdb_iso': '6050.e', 'lmfdb_label': '6050.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -8, 1], 'min_quad_twist_disc': 5, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '8.2.0.b.1', '24.8.0.b.1', '33.8.0-3.a.1.2', '264.16.0.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.47313068782177014703954425991', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 3025], [3, 2, 3025], [5, 14, 242], [11, 32, 50]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1299973703172128310272597719', 'prec': 103}, 'szpiro_ratio': 3.1599617190045772, '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, -1, -2, 1, 0, 2, 1, -1, 1, 0, 0, -2, 4, -1, 0, 1, 6, -1, -2, 0], 'aplist': [-1, -2, 0, 1, 0, 4, 6, -2, -3, -6, -7, -4, -9, 4, 9, 0, 6, 10, -10, 0, -11, -8, -12, 15, 17], 'class_deg': 3, 'class_size': 2, 'conductor': 6050, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '6050.e', 'trace_hash': 227918671329050196}
• 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': '0.50397888823511773282005925265', 'prec': 103}, 'conductor': 6050, 'gens': [[2, 11, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.47313068782177014703954425991', 'prec': 103}], 'lmfdb_label': '6050.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.5296748395953630098712335668', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1712083270042300621952117786747266916', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': [2, 52]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [12, 0], '3': [3, 0], '5': 'a', '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '6050.e2'}
• ec_torsion_growth •

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

  
  
  • id: 315473
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '6050.e2', 'torsion': [3]}
  • id: 315474
    {'degree': 3, 'field': [2, -18, -1, 1], 'lmfdb_label': '6050.e2', 'torsion': [2]}
  • id: 315475
    {'degree': 6, 'field': [-512, -128, 328, 48, -41, -2, 1], 'lmfdb_label': '6050.e2', 'torsion': [2, 2]}
  • id: 315476
    {'degree': 6, 'field': [-204, -93, 91, 3, 1, -3, 1], 'lmfdb_label': '6050.e2', 'torsion': [3]}
  • id: 315477
    {'degree': 6, 'field': [939, 698, 100, 40, 20, -2, 1], 'lmfdb_label': '6050.e2', 'torsion': [6]}
  • id: 315480
    {'degree': 12, 'field': [4412, -6288, 8478, -18424, 22635, -13372, 3962, -1016, 437, -100, 8, -4, 1], 'lmfdb_label': '6050.e2', 'torsion': [2, 6]}
  • id: 315479
    {'degree': 12, 'field': [41616, 18972, 27213, -7239, 8764, 1071, -769, 456, -81, -9, 8, -3, 1], 'lmfdb_label': '6050.e2', 'torsion': [3, 3]}
  • id: 315478
    {'degree': 12, 'field': [113188, -183804, -80968, 18522, -5061, 4020, 1054, 558, -179, 8, -6, -6, 1], 'lmfdb_label': '6050.e2', 'torsion': [4]}
  • id: 315482
    {'degree': 18, 'field': [5184, 148608, -504000, 373968, 93324, -61020, -123908, 50060, -6485, 32861, -21106, -2599, 6385, -1742, -247, 193, -20, -5, 1], 'lmfdb_label': '6050.e2', 'torsion': [6]}
  • id: 315481
    {'degree': 18, 'field': [639241, -1668033, 2005857, -1706098, 1220208, -650346, 313960, -134298, 43635, -24145, 9645, -5058, 2150, -276, 228, -28, 27, -3, 1], 'lmfdb_label': '6050.e2', 'torsion': [9]}
• 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: 120395
    {'conductor': 6050, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '6050.e2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 120396
    {'conductor': 6050, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '6050.e2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 120397
    {'conductor': 6050, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '6050.e2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1703640
    {'adelic_gens': [[78, 193, 121, 243], [3, 4, 8, 11], [4, 3, 9, 7], [1, 0, 6, 1], [171, 2, 130, 7], [133, 6, 135, 19], [259, 6, 258, 7], [199, 6, 0, 1], [261, 262, 254, 257], [1, 6, 0, 1]], 'adelic_image': '264.16.0.?', 'conductor': 6050, 'lmfdb_label': '6050.e2', 'prime': 0}
  • id: 29803
    {'conductor': 6050, 'elladic_image': '8.2.0.2', 'lmfdb_label': '6050.e2', 'modell_image': '2G', 'prime': 2}
  • id: 29804
    {'conductor': 6050, 'elladic_image': '3.4.0.1', 'lmfdb_label': '6050.e2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 234319
    {'lmfdb_iso': '6050.e', 'p': 7, 'prec': 20, 'unit': 68156352429713546, 'val': -1}
  • id: 234323
    {'lmfdb_iso': '6050.e', 'p': 13, 'prec': 20, 'unit': 995752671963815107255, 'val': 1}
  • id: 234325
    {'lmfdb_iso': '6050.e', 'p': 17, 'prec': 20, 'unit': 148930004899583275234869, 'val': 1}
  • id: 234326
    {'lmfdb_iso': '6050.e', 'p': 19, 'prec': 20, 'unit': 1555574407453588769427547, 'val': 1}
  • id: 234329
    {'lmfdb_iso': '6050.e', 'p': 23, 'prec': 20, 'unit': 1588626250821867510451796, 'val': 1}
  • id: 234322
    {'lmfdb_iso': '6050.e', 'p': 29, 'prec': 20, 'unit': 471009385091840891308538269, 'val': 1}
  • id: 234333
    {'lmfdb_iso': '6050.e', 'p': 31, 'prec': 20, 'unit': 1863373474169615161732697030, 'val': 1}
  • id: 234318
    {'lmfdb_iso': '6050.e', 'p': 37, 'prec': 20, 'unit': 51314725216312268769346872389, 'val': 1}
  • id: 234320
    {'lmfdb_iso': '6050.e', 'p': 41, 'prec': 20, 'unit': 1226486188897018397151046454196, 'val': 1}
  • id: 234321
    {'lmfdb_iso': '6050.e', 'p': 43, 'prec': 20, 'unit': 4491413874957703980310862829932, 'val': 1}
  • id: 234331
    {'lmfdb_iso': '6050.e', 'p': 47, 'prec': 20, 'unit': 51448488263759707629374711859183, 'val': 1}
  • id: 234327
    {'lmfdb_iso': '6050.e', 'p': 59, 'prec': 20, 'unit': 2086523224242830809909007008481199, 'val': 1}
  • id: 234332
    {'lmfdb_iso': '6050.e', 'p': 61, 'prec': 20, 'unit': 332903550273620547870737643002689, 'val': 1}
  • id: 234317
    {'lmfdb_iso': '6050.e', 'p': 67, 'prec': 20, 'unit': 42208517042208730491332626510793190, 'val': 1}
  • id: 234328
    {'lmfdb_iso': '6050.e', 'p': 73, 'prec': 20, 'unit': 97301941520121881035547234379439157, 'val': 1}
  • id: 234324
    {'lmfdb_iso': '6050.e', 'p': 79, 'prec': 20, 'unit': 1052459101361738000300870362692068133, 'val': 1}
  • id: 234316
    {'lmfdb_iso': '6050.e', 'p': 83, 'prec': 20, 'unit': 1278007864711765753936572661643926340, 'val': 1}
  • id: 234330
    {'lmfdb_iso': '6050.e', 'p': 89, 'prec': 20, 'unit': 1180899350577632218582713519965883179, 'val': 1}
  • id: 234315
    {'lmfdb_iso': '6050.e', 'p': 97, 'prec': 20, 'unit': 5146075703835024584331229906271645238, 'val': 1}