Elliptic curve data - 311696.g1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '311696g', 'Clabel': '311696g2', 'Cnumber': 2, 'abc_quality': 0.8713684246171298, 'absD': 2044466428928, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 644, 'ainvs': [0, 1, 0, -59088, 5508292], 'analytic_rank': 2, 'bad_primes': [2, 7, 11, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 311696, 'degree': 819200, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4021923295131948925933509815', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2], 'jinv': [12576878500, 1127], 'lmfdb_iso': '311696.g', 'lmfdb_label': '311696.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -488, 4316], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '92.6.0.?', '644.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 11, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '2.8879686545587108834340935064', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37437795735261147061864757536', 'prec': 107}, 'szpiro_ratio': 3.523694211829201, '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, 0, 0, -1, 0, 1, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, -2, 0, -1, 0, -6, 0, 0, -1, -2, -2, 2, 6, 4, 2, 14, -14, -12, 4, 0, 2, -8, -4, -16, 4], 'class_deg': 2, 'class_size': 2, 'conductor': 311696, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '311696.g', 'trace_hash': 774100355648302382}
• 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': '0.060544014925692216712861654786', 'prec': 107}, 'conductor': 311696, 'gens': [[128, 242, 1], [111, 574, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.89095448327360009317668451419', 'prec': 103}, {'__RealLiteral__': 0, 'data': '3.3933027221138701907606197519', 'prec': 100}], 'lmfdb_label': '311696.g1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.79086936671503754959103112085', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.1360237636949068648407563670620711973', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[139, 0, 1]], 'xcoord_integral_points': [111, 128, 139, 143, 216, 2064]}
• lmfdb_label 311696.g1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13145629
    {'degree': 2, 'field': [-23, 0, 1], 'lmfdb_label': '311696.g1', 'torsion': [2, 2]}
  • id: 13145630
    {'degree': 4, 'field': [718, 16, -51, -1, 1], 'lmfdb_label': '311696.g1', 'torsion': [4]}
  • id: 13145633
    {'degree': 8, 'field': [-14231052, 0, -793276, 0, -13068, 0, 0, 0, 1], 'lmfdb_label': '311696.g1', 'torsion': [6]}
  • id: 13145631
    {'degree': 8, 'field': [-36659, 64114, -33168, 5058, -294, 334, -72, -2, 1], 'lmfdb_label': '311696.g1', 'torsion': [2, 4]}
  • id: 13145632
    {'degree': 8, 'field': [361, -798, 3410, -2608, 2647, -200, 82, -2, 1], 'lmfdb_label': '311696.g1', 'torsion': [2, 4]}
  • id: 13145634
    {'degree': 16, 'field': [2299552187, -573954370, 285319537, -264213806, 229820780, -118513946, 38671583, -13058710, 3189096, -792598, 207775, -20922, 1712, -14, -47, -2, 1], 'lmfdb_label': '311696.g1', 'torsion': [8]}
  • id: 13145635
    {'degree': 16, 'field': [187980912144, 202662837216, 920659074336, 571565790816, 70132873728, 4080155760, -1719013328, -460401008, 25314344, -4077832, 164608, 63624, -9476, 532, -28, -4, 1], 'lmfdb_label': '311696.g1', 'torsion': [2, 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: 7719072
    {'conductor': 311696, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '311696.g1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7719073
    {'conductor': 311696, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '311696.g1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7719074
    {'conductor': 311696, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '311696.g1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7719075
    {'conductor': 311696, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '311696.g1', 'prime': 23, 'reduction_type': -1, '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: 3620823
    {'adelic_gens': [[1, 2, 2, 5], [1, 4, 0, 1], [562, 1, 363, 0], [484, 165, 161, 484], [641, 4, 640, 5], [1, 0, 4, 1], [185, 4, 370, 9], [3, 4, 8, 11]], 'adelic_image': '644.12.0.?', 'conductor': 311696, 'lmfdb_label': '311696.g1', 'prime': 0}
  • id: 1094027
    {'conductor': 311696, 'elladic_image': '2.3.0.1', 'lmfdb_label': '311696.g1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 311696.g does not appear in ec_padic