Elliptic curve data - 210210.bl4

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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': '210210eb', 'Clabel': '210210eb4', 'Cnumber': 4, 'abc_quality': 0.9533105316105353, 'absD': 1886191470459673076700, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 24024, 'ainvs': [1, 0, 1, 2656166, 1261138232], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 210210, 'degree': 11796480, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7697264389925049865361718952', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 37, 'isogeny_degrees': [1, 2, 4], 'jinv': [17615758461429817079, 16032362964918300], 'lmfdb_iso': '210210.bl', 'lmfdb_label': '210210.bl4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 54208, -3653556], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.3', '286.6.0.?', '308.12.0.?', '364.12.0.?', '572.12.0.?', '1848.24.0.?', '2184.24.0.?', '3432.24.0.?', '4004.24.0.?', '24024.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 7007], [3, 4, 70070], [5, 6, 42042], [7, 32, 4290], [11, 12, 19110], [13, 14, 16170]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7967713644648483339834955235', 'prec': 100}, 'szpiro_ratio': 4.568490165800837, '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, -1, -1, 0, -1, 1, 1, -1, 1, 1, 0, -1, 1, -2, -1, 4, -1], 'aplist': [-1, 1, -1, 0, -1, 1, -2, 4, 0, -6, 0, -2, 10, -4, -4, 6, 0, -2, 8, 8, -6, -8, -12, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 210210, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '210210.bl', 'trace_hash': 482096816506819430}
• 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': '0.0039286757153766826386475520025', 'prec': 110}, 'conductor': 210210, 'gens': [], 'heights': [], 'lmfdb_label': '210210.bl4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.096742889488017473642860225920', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5478862318082795782857636147205760030', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-1769, 1765, 2]], 'xcoord_integral_points': []}
• lmfdb_label 210210.bl4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9188769
    {'degree': 2, 'field': [-91, 0, 1], 'lmfdb_label': '210210.bl4', 'torsion': [4]}
  • id: 9188768
    {'degree': 2, 'field': [36, -1, 1], 'lmfdb_label': '210210.bl4', 'torsion': [2, 2]}
  • id: 9188770
    {'degree': 2, 'field': [77, 0, 1], 'lmfdb_label': '210210.bl4', 'torsion': [4]}
  • id: 9188771
    {'degree': 4, 'field': [1764, 0, -7, 0, 1], 'lmfdb_label': '210210.bl4', 'torsion': [2, 4]}
  • id: 9188775
    {'degree': 8, 'field': [-5436002, -142195, 134092, 16205, -8099, -7, 7, -4, 1], 'lmfdb_label': '210210.bl4', 'torsion': [6]}
  • id: 9188774
    {'degree': 8, 'field': [576, -1440, 2184, -3636, 3625, -2, 63, -2, 1], 'lmfdb_label': '210210.bl4', 'torsion': [8]}
  • id: 9188773
    {'degree': 8, 'field': [204490000, 0, -3718000, 0, -195975, 0, 260, 0, 1], 'lmfdb_label': '210210.bl4', 'torsion': [8]}
  • id: 9188772
    {'degree': 8, 'field': [204490000, 0, 0, 0, 1129700, 0, 0, 0, 1], 'lmfdb_label': '210210.bl4', 'torsion': [2, 4]}
  • id: 9188777
    {'degree': 16, 'field': [1666598976, 3466937376, 5228815032, 4983323436, 3215495305, -669431816, 79649486, 5376764, -789954, -367794, 111378, -5292, -1122, 344, 14, -2, 1], 'lmfdb_label': '210210.bl4', 'torsion': [2, 8]}
  • id: 9188779
    {'degree': 16, 'field': [2140628896800, -976102289280, 1196992698546, -322682870565, 88087548468, -43802717878, 6845131577, -743564809, 534419372, 23576081, 8553545, -13892, 1315, -4523, -92, -2, 1], 'lmfdb_label': '210210.bl4', 'torsion': [2, 6]}
  • id: 9188780
    {'degree': 16, 'field': [9161457704100, 0, -209962032579, 0, -869479650, 0, -5360158297, 0, 156869687, 0, -475345, 0, 10855, 0, -182, 0, 1], 'lmfdb_label': '210210.bl4', 'torsion': [12]}
  • id: 9188781
    {'degree': 16, 'field': [98768097509796, 0, 824986051461, 0, 41670931302, 0, 3208196783, 0, -6014305, 0, 1360007, 0, -1793, 0, 154, 0, 1], 'lmfdb_label': '210210.bl4', 'torsion': [12]}
  • id: 9188776
    {'degree': 16, 'field': [156205028236401, 0, 43633157124708, 0, -6738753857522, 0, 318355623356, 0, 79799044395, 0, 1129756, 0, -564822, 0, 8, 0, 1], 'lmfdb_label': '210210.bl4', 'torsion': [4, 4]}
  • id: 9188778
    {'degree': 16, 'field': [12386325583009440000, 0, -10417168837512000, 0, -607549293049500, 0, 2688100381860, 0, 14582923801, 0, -63773488, 0, -69486, 0, 668, 0, 1], 'lmfdb_label': '210210.bl4', 'torsion': [2, 8]}
• 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: 5210006
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '210210.bl4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5210007
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '210210.bl4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5210008
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '210210.bl4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5210009
    {'conductor': 210210, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '210210.bl4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5210010
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '210210.bl4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5210011
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '210210.bl4', 'prime': 13, '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: 3008847
    {'adelic_gens': [[20591, 24016, 10292, 23991], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 24018, 24019], [3011, 3004, 3050, 15021], [15019, 15018, 21034, 9019], [7400, 3, 16637, 2], [8009, 8, 8012, 33], [24017, 8, 24016, 9], [17476, 1, 4391, 6]], 'adelic_image': '24024.48.0.?', 'conductor': 210210, 'lmfdb_label': '210210.bl4', 'prime': 0}
  • id: 775485
    {'conductor': 210210, 'elladic_image': '4.6.0.1', 'lmfdb_label': '210210.bl4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 210210.bl does not appear in ec_padic