Elliptic curve data - 6050.r1

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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': '6050i', 'Clabel': '6050i2', 'Cnumber': 2, 'abc_quality': 0.9698671811062001, 'absD': 10717944050, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 120, 'ainvs': [1, 1, 0, -67520, -6781210], 'analytic_rank': 0, 'bad_primes': [2, 5, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 6050, 'degree': 19008, 'elladic_images': ['8.2.0.2', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2861452746214391064784517874', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 17, 'isogeny_degrees': [1, 3], 'jinv': [6352571665, 2], 'lmfdb_iso': '6050.r', 'lmfdb_label': '6050.r1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -558, 4841], 'min_quad_twist_disc': -11, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '8.2.0.b.1', '15.8.0-3.a.1.1', '24.8.0.b.1', '120.16.0.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3025], [5, 10, 242], [11, 52, 50]], 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.58069122598315798532963715345', 'prec': 107}, 'szpiro_ratio': 5.164805527610552, '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.r', 'trace_hash': 1689167371360027756}
• 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': '0.076360437611381474669705947371', 'prec': 107}, 'conductor': 6050, 'gens': [], 'heights': [], 'lmfdb_label': '6050.r1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29616969422719488180973732017', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6655272480447539362876358815172532079', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [2, 1], '5': 'a', '7': [2, 0], '11': 'a', '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '6050.r1'}
• ec_torsion_growth •

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

  
  
  • id: 315362
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '6050.r1', 'torsion': [3]}
  • id: 315363
    {'degree': 3, 'field': [2, -18, -1, 1], 'lmfdb_label': '6050.r1', 'torsion': [2]}
  • id: 315364
    {'degree': 6, 'field': [-512, -128, 328, 48, -41, -2, 1], 'lmfdb_label': '6050.r1', 'torsion': [2, 2]}
  • id: 315366
    {'degree': 6, 'field': [1896, -366, 370, 25, -25, -1, 1], 'lmfdb_label': '6050.r1', 'torsion': [6]}
  • id: 315365
    {'degree': 6, 'field': [49279, -1983, 660, -435, 0, -3, 1], 'lmfdb_label': '6050.r1', 'torsion': [3]}
  • id: 315367
    {'degree': 12, 'field': [24200, 0, 42350, 0, -12375, 0, 2400, 0, -590, 0, 10, 0, 1], 'lmfdb_label': '6050.r1', 'torsion': [4]}
  • id: 315369
    {'degree': 12, 'field': [6267136, -478848, 151344, -236800, 162890, 26012, -12751, -3202, 1665, 120, -61, -2, 1], 'lmfdb_label': '6050.r1', 'torsion': [2, 6]}
  • id: 315368
    {'degree': 12, 'field': [2428419841, -97720257, -28591851, 41563950, -427005, -434937, 281834, 1977, -1965, 870, 9, -3, 1], 'lmfdb_label': '6050.r1', 'torsion': [3, 3]}
  • id: 315370
    {'degree': 18, 'field': [8991744, 9105408, 14745600, 6418752, 5280960, -1406592, 171556, -1148220, 12384, -132110, 50490, -2790, 12225, -150, 1395, -98, 54, 0, 1], 'lmfdb_label': '6050.r1', 'torsion': [9]}
  • id: 315371
    {'degree': 18, 'field': [35103231, -50906457, 29629269, -11996796, 1378890, -713442, 1260034, -253008, 8037, 129645, -35541, -1488, -2674, 2286, -810, 84, 27, -9, 1], 'lmfdb_label': '6050.r1', 'torsion': [6]}
• 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: 120353
    {'conductor': 6050, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6050.r1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 120354
    {'conductor': 6050, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '6050.r1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 120355
    {'conductor': 6050, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '6050.r1', '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: 1703662
    {'adelic_gens': [[98, 27, 55, 67], [51, 2, 10, 7], [61, 6, 63, 19], [1, 0, 6, 1], [4, 3, 9, 7], [115, 6, 114, 7], [31, 6, 0, 1], [3, 4, 8, 11], [117, 118, 110, 113], [1, 6, 0, 1]], 'adelic_image': '120.16.0.?', 'conductor': 6050, 'lmfdb_label': '6050.r1', 'prime': 0}
  • id: 29832
    {'conductor': 6050, 'elladic_image': '8.2.0.2', 'lmfdb_label': '6050.r1', 'modell_image': '2G', 'prime': 2}
  • id: 29833
    {'conductor': 6050, 'elladic_image': '3.4.0.1', 'lmfdb_label': '6050.r1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 6050.r does not appear in ec_padic