Elliptic curve data - 1650.b4

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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': '1650a', 'Clabel': '1650a2', 'Cnumber': 2, 'abc_quality': 0.9379136566213516, 'absD': 61256250000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1320, 'ainvs': [1, 1, 0, -1875, 28125], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 1650, 'degree': 1536, 'elladic_images': ['8.24.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.81166041613950851056934219527', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [46694890801, 3920400], 'lmfdb_iso': '1650.b', 'lmfdb_label': '1650.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -75, 225], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0-4.b.1.8', '20.24.0-4.b.1.3', '24.48.0-24.l.1.20', '40.48.0-40.i.2.8', '44.24.0-4.b.1.2', '88.48.0.?', '120.96.0.?', '220.48.0.?', '264.96.0.?', '440.96.0.?', '1320.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 14, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.86044701373778127007026952767', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 25], [3, 4, 550], [5, 18, 66], [11, 12, 150]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.0069414599224583232689625286569', 'prec': 110}, 'szpiro_ratio': 4.619475853751714, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, -1, 1, 0, -1, -1, 2, 0, 0, 1, -2, -1, -4, 0], 'aplist': [-1, -1, 0, 0, -1, 2, -2, -4, 0, -2, 0, 2, 2, 12, -8, -6, -12, 6, -4, 0, 6, -16, -4, 10, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 1650, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '1650.b', 'trace_hash': 1694871926204612899}
• 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': '0.19724260069502617237108061578', 'prec': 103}, 'conductor': 1650, 'gens': [[5, 135, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.86044701373778127007026952767', 'prec': 103}], 'lmfdb_label': '1650.b4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0817510997646955668372275933', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999999', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8615790068001860072474845502465708774', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-50, 25, 1], [30, -15, 1]], 'xcoord_integral_points': [-50, -6, 5, 30, 31, 50, 75, 930]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [5, 0], '5': 'a', '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1650.b4'}
• ec_torsion_growth •

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

  
  
  • id: 82163
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '1650.b4', 'torsion': [2, 4]}
  • id: 82164
    {'degree': 4, 'field': [9, -16, 17, -2, 1], 'lmfdb_label': '1650.b4', 'torsion': [2, 4]}
  • id: 82165
    {'degree': 4, 'field': [16, 0, -3, 0, 1], 'lmfdb_label': '1650.b4', 'torsion': [2, 4]}
  • id: 82167
    {'degree': 8, 'field': [-149, 532, -284, -464, 153, 92, -26, -4, 1], 'lmfdb_label': '1650.b4', 'torsion': [2, 8]}
  • id: 82168
    {'degree': 8, 'field': [16, 0, 24, 0, 32, 0, 6, 0, 1], 'lmfdb_label': '1650.b4', 'torsion': [2, 8]}
  • id: 82166
    {'degree': 8, 'field': [20, -100, 186, -190, 141, -58, 24, -4, 1], 'lmfdb_label': '1650.b4', 'torsion': [4, 4]}
  • id: 82169
    {'degree': 8, 'field': [26, -131, 122, 17, -5, -7, 7, -4, 1], 'lmfdb_label': '1650.b4', 'torsion': [2, 6]}
  • id: 82170
    {'degree': 16, 'field': [256, 0, 0, 0, 2016, 0, 0, 0, 481, 0, 0, 0, 126, 0, 0, 0, 1], 'lmfdb_label': '1650.b4', 'torsion': [4, 8]}
  • id: 82172
    {'degree': 16, 'field': [22500, 0, -36000, 0, 14400, 0, -10625, 0, 5150, 0, 115, 0, 25, 0, -10, 0, 1], 'lmfdb_label': '1650.b4', 'torsion': [2, 12]}
  • id: 82171
    {'degree': 16, 'field': [245025, 0, -653400, 0, 689040, 0, -302280, 0, 50686, 0, -2184, 0, 656, 0, -24, 0, 1], 'lmfdb_label': '1650.b4', '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: 25747
    {'conductor': 1650, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1650.b4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 25748
    {'conductor': 1650, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1650.b4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 25749
    {'conductor': 1650, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '1650.b4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 25750
    {'conductor': 1650, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1650.b4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1674758
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1313, 8, 1312, 9], [881, 8, 884, 33], [487, 6, 714, 1315], [3, 994, 1316, 325], [521, 1318, 546, 5], [5, 4, 1316, 1317], [665, 332, 332, 661]], 'adelic_image': '1320.192.1.?', 'conductor': 1650, 'lmfdb_label': '1650.b4', 'prime': 0}
  • id: 7969
    {'conductor': 1650, 'elladic_image': '8.24.0.11', 'lmfdb_label': '1650.b4', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 44696
    {'lmfdb_iso': '1650.b', 'p': 13, 'prec': 20, 'unit': 623412231691468044045, 'val': 1}
  • id: 44698
    {'lmfdb_iso': '1650.b', 'p': 17, 'prec': 20, 'unit': 75960262157135306616351, 'val': 1}
  • id: 44699
    {'lmfdb_iso': '1650.b', 'p': 19, 'prec': 20, 'unit': 1790609514027501669212492, 'val': 1}
  • id: 44695
    {'lmfdb_iso': '1650.b', 'p': 29, 'prec': 20, 'unit': 3453814321880825273858601684, 'val': 1}
  • id: 44692
    {'lmfdb_iso': '1650.b', 'p': 37, 'prec': 20, 'unit': 253940249715710585143227838480, 'val': 1}
  • id: 44693
    {'lmfdb_iso': '1650.b', 'p': 41, 'prec': 20, 'unit': 2547551323474929878685686793880, 'val': 1}
  • id: 44694
    {'lmfdb_iso': '1650.b', 'p': 43, 'prec': 20, 'unit': 6473065690265784959860259822547, 'val': 1}
  • id: 44704
    {'lmfdb_iso': '1650.b', 'p': 47, 'prec': 20, 'unit': 49032065044476330586830741658073, 'val': 1}
  • id: 44700
    {'lmfdb_iso': '1650.b', 'p': 53, 'prec': 20, 'unit': 573155551870829751938859535702146, 'val': 1}
  • id: 44701
    {'lmfdb_iso': '1650.b', 'p': 59, 'prec': 20, 'unit': 3845795154534738681894404768847776, 'val': 1}
  • id: 44705
    {'lmfdb_iso': '1650.b', 'p': 61, 'prec': 20, 'unit': 4356737289284580281192138335833361, 'val': 1}
  • id: 44691
    {'lmfdb_iso': '1650.b', 'p': 67, 'prec': 20, 'unit': 20240850406708184909634074733508588, 'val': 1}
  • id: 44702
    {'lmfdb_iso': '1650.b', 'p': 73, 'prec': 20, 'unit': 148397948407114159369765809064827365, 'val': 1}
  • id: 44697
    {'lmfdb_iso': '1650.b', 'p': 79, 'prec': 20, 'unit': 475759339423299704363698549886949364, 'val': 1}
  • id: 44690
    {'lmfdb_iso': '1650.b', 'p': 83, 'prec': 20, 'unit': 1483661639380812368494031507744454119, 'val': 1}
  • id: 44703
    {'lmfdb_iso': '1650.b', 'p': 89, 'prec': 20, 'unit': 4608284903963133034301948170138212872, 'val': 1}
  • id: 44689
    {'lmfdb_iso': '1650.b', 'p': 97, 'prec': 20, 'unit': 34015333712952424478355189640229543019, 'val': 1}