Elliptic curve data - 15210.v4

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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': '15210v', 'Clabel': '15210v4', 'Cnumber': 4, 'abc_quality': 1.0187728994158647, 'absD': 27174886486861838400, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [1, -1, 0, 171081, 249282333], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 15210, 'degree': 580608, 'elladic_images': ['4.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4088038158224594540228188447', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [157376536199, 7722894400], 'lmfdb_iso': '15210.v', 'lmfdb_label': '15210.v4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 112, -4194], 'min_quad_twist_disc': -39, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.a.1', '6.12.0.a.1', '12.48.0.b.2', '39.8.0-3.a.1.1', '60.96.0-12.b.2.3', '78.24.0.?', '156.96.0.?', '260.12.0.?', '520.24.0.?', '780.192.3.?', '1560.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.2953654430584498894762998631', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1521], [3, 6, 845], [5, 6, 3042], [13, 98, 90]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.57702299275763624029845250546', 'prec': 103}, 'szpiro_ratio': 5.419861113761531, '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, 0, 1, 1, 0, 4, -1, 0, -1, -6, 0, 0, -4, 0, 1, 6, 0, -2, 1], 'aplist': [-1, 0, 1, 4, -6, 0, 6, -2, -6, 6, -2, -2, -6, 2, -12, -6, 6, 2, 4, -6, 10, -4, 0, -6, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 15210, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '15210.v', 'trace_hash': 2272820935318703733}
• 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': '0.0080861089686295505273407336251', 'prec': 110}, 'conductor': 15210, 'gens': [[-146, 14945, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.2953654430584498894762998631', 'prec': 100}], 'lmfdb_label': '15210.v4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16013111574074840649585747555', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2215243613636423339242301858184265049', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-2157, 2157, 2]], 'xcoord_integral_points': [-146]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 1], '3': 'a', '5': [4, 0], '7': [1, 0], '11': [1, 0], '13': 'a', '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': '15210.v4'}
• ec_torsion_growth •

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

  
  
  • id: 782160
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '15210.v4', 'torsion': [6]}
  • id: 782159
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '15210.v4', 'torsion': [2, 2]}
  • id: 782161
    {'degree': 4, 'field': [4, 28, -7, -1, 1], 'lmfdb_label': '15210.v4', 'torsion': [4]}
  • id: 782162
    {'degree': 4, 'field': [9, 0, 7, 0, 1], 'lmfdb_label': '15210.v4', 'torsion': [2, 6]}
  • id: 782163
    {'degree': 6, 'field': [1170, -585, 315, -51, 33, -3, 1], 'lmfdb_label': '15210.v4', 'torsion': [6]}
  • id: 782164
    {'degree': 8, 'field': [16, 0, 840, 0, 113, 0, 15, 0, 1], 'lmfdb_label': '15210.v4', 'torsion': [2, 4]}
  • id: 782165
    {'degree': 8, 'field': [25, -30, 3, 46, 52, 12, -5, -4, 1], 'lmfdb_label': '15210.v4', 'torsion': [2, 4]}
  • id: 782166
    {'degree': 8, 'field': [196, 0, -180, 0, 77, 0, -15, 0, 1], 'lmfdb_label': '15210.v4', 'torsion': [12]}
  • id: 782167
    {'degree': 12, 'field': [2304, -6336, 15840, -5028, 2301, -1497, -53, 24, 24, 4, 15, -3, 1], 'lmfdb_label': '15210.v4', 'torsion': [3, 6]}
  • id: 782168
    {'degree': 12, 'field': [774400, 0, -606975, 0, 174975, 0, -19399, 0, 1353, 0, -57, 0, 1], 'lmfdb_label': '15210.v4', 'torsion': [2, 6]}
  • id: 782172
    {'degree': 16, 'field': [16, 16, 24, -88, -48, -76, 210, 18, 71, -192, 73, -38, 46, -20, 7, -4, 1], 'lmfdb_label': '15210.v4', 'torsion': [2, 12]}
  • id: 782171
    {'degree': 16, 'field': [4900, -7700, -1110, 5450, -2129, 558, 463, -966, 907, 54, -352, 164, 33, -24, 7, 0, 1], 'lmfdb_label': '15210.v4', 'torsion': [2, 12]}
  • id: 782169
    {'degree': 16, 'field': [8836, 0, 2836, 0, 17269, 0, 9659, 0, 1395, 0, -26, 0, 19, 0, 11, 0, 1], 'lmfdb_label': '15210.v4', 'torsion': [4, 4]}
  • id: 782170
    {'degree': 16, 'field': [51265600, 0, 10737600, 0, -6740320, 0, -386800, 0, 171576, 0, -16516, 0, 801, 0, -16, 0, 1], 'lmfdb_label': '15210.v4', 'torsion': [8]}
  • id: 782173
    {'degree': 18, 'field': [14033967, -126085113, 305782785, -247537656, -46392198, 160032834, -65878786, 6255192, 1074345, -1308991, 731511, -193224, 42834, -8814, 726, 40, 15, -9, 1], 'lmfdb_label': '15210.v4', 'torsion': [18]}
• 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: 336339
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '15210.v4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 336340
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '15210.v4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 336341
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '15210.v4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 336342
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '15210.v4', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1765335
    {'adelic_gens': [[13, 24, 852, 253], [1537, 24, 1536, 25], [479, 1554, 1068, 1487], [781, 24, 0, 1], [391, 24, 195, 1], [1, 24, 0, 1], [15, 16, 314, 335], [1039, 1536, 260, 1559], [1, 0, 24, 1], [957, 10, 524, 101]], 'adelic_image': '1560.384.9.?', 'conductor': 15210, 'lmfdb_label': '15210.v4', 'prime': 0}
  • id: 71928
    {'conductor': 15210, 'elladic_image': '4.6.0.5', 'lmfdb_label': '15210.v4', 'modell_image': '2B', 'prime': 2}
  • id: 71929
    {'conductor': 15210, 'elladic_image': '3.4.0.1', 'lmfdb_label': '15210.v4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 683522
    {'lmfdb_iso': '15210.v', 'p': 7, 'prec': 20, 'unit': 9489106621159176, 'val': 1}
  • id: 683527
    {'lmfdb_iso': '15210.v', 'p': 11, 'prec': 20, 'unit': 27028538997516739928, 'val': 1}
  • id: 683528
    {'lmfdb_iso': '15210.v', 'p': 17, 'prec': 20, 'unit': 44310225178692725274348, 'val': 1}
  • id: 683529
    {'lmfdb_iso': '15210.v', 'p': 19, 'prec': 20, 'unit': 203399688163470534591002, 'val': 1}
  • id: 683533
    {'lmfdb_iso': '15210.v', 'p': 23, 'prec': 20, 'unit': 41376814552390819888199797, 'val': 1}
  • id: 683525
    {'lmfdb_iso': '15210.v', 'p': 29, 'prec': 20, 'unit': 5395739668250724579684472177, 'val': 1}
  • id: 683538
    {'lmfdb_iso': '15210.v', 'p': 31, 'prec': 20, 'unit': 12724765980638925323861517961, 'val': 1}
  • id: 683521
    {'lmfdb_iso': '15210.v', 'p': 37, 'prec': 20, 'unit': 607439567907215275422314986523, 'val': 1}
  • id: 683523
    {'lmfdb_iso': '15210.v', 'p': 41, 'prec': 20, 'unit': 1350605646665450023453447574602, 'val': 1}
  • id: 683524
    {'lmfdb_iso': '15210.v', 'p': 43, 'prec': 20, 'unit': 4848899572957381081687934376176, 'val': 1}
  • id: 683536
    {'lmfdb_iso': '15210.v', 'p': 47, 'prec': 20, 'unit': 37191438539151635961977640138011, 'val': 1}
  • id: 683530
    {'lmfdb_iso': '15210.v', 'p': 53, 'prec': 20, 'unit': 401037633867879907299941466940068, 'val': 1}
  • id: 683531
    {'lmfdb_iso': '15210.v', 'p': 59, 'prec': 20, 'unit': 3954778133243605563430449833333512, 'val': 1}
  • id: 683537
    {'lmfdb_iso': '15210.v', 'p': 61, 'prec': 20, 'unit': 521457176516356467369243844964667, 'val': 1}
  • id: 683520
    {'lmfdb_iso': '15210.v', 'p': 67, 'prec': 20, 'unit': 46180011883685004597395234283798952, 'val': 1}
  • id: 683535
    {'lmfdb_iso': '15210.v', 'p': 71, 'prec': 20, 'unit': 134163360391828098138979392206023095, 'val': 1}
  • id: 683532
    {'lmfdb_iso': '15210.v', 'p': 73, 'prec': 20, 'unit': 100196919763680127087810268724632928, 'val': 1}
  • id: 683526
    {'lmfdb_iso': '15210.v', 'p': 79, 'prec': 20, 'unit': 51283203631262629254883252108124388, 'val': 1}
  • id: 683534
    {'lmfdb_iso': '15210.v', 'p': 89, 'prec': 20, 'unit': 664716574483651964226544989641819708, 'val': 1}
  • id: 683519
    {'lmfdb_iso': '15210.v', 'p': 97, 'prec': 20, 'unit': 25853912670507536214647138734316132627, 'val': 1}