Elliptic curve data - 5070.t4

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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': '5070t', 'Clabel': '5070t1', 'Cnumber': 1, 'abc_quality': 1.102611128088335, 'absD': 19761264961776000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1560, 'ainvs': [1, 0, 0, 675574, 8108580], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 5070, 'degree': 120960, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3919809976976821723337239594', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [7064514799444439, 4094064000000], 'lmfdb_iso': '5070.t', 'lmfdb_label': '5070.t4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 3997, 3998], 'min_quad_twist_disc': 13, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.24.0-6.a.1.3', '39.8.0-3.a.1.1', '40.6.0.c.1', '78.48.0.?', '120.48.0.?', '1560.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 15, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.25503608223036862659117698646', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 507], [3, 4, 338], [5, 6, 507], [13, 98, 30]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1095063189669138043069802386', 'prec': 100}, 'szpiro_ratio': 6.081698798067971, '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, -2, 1, 1, -1, 0, 1, 0, -2, -1, 1, 0, 1, -2, -1], 'aplist': [1, 1, -1, -2, 0, 0, 0, -2, -6, 0, -8, -2, -6, -4, 0, -6, 0, 14, 4, 0, 4, -16, 12, 6, 4], 'class_deg': 6, 'class_size': 4, 'conductor': 5070, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '5070.t', 'trace_hash': 730738306333318081}
• 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': '0.0083627998690087505167273148321', 'prec': 110}, 'conductor': 5070, 'gens': [[196, 12070, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.25503608223036862659117698646', 'prec': 103}], 'lmfdb_label': '5070.t4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12997156027386942001329828371', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.9665387560508572652813787088734685062', 'prec': 130}, 'tamagawa_product': 720, 'torsion_generators': [[-12, 6, 1]], 'xcoord_integral_points': [-12, 4, 196, 664, 988, 3238, 6280, 42238]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': 'a', '17': [1, 3, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '5070.t4'}
• ec_torsion_growth •

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

  
  
  • id: 265679
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '5070.t4', 'torsion': [6]}
  • id: 265678
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '5070.t4', 'torsion': [2, 2]}
  • id: 265680
    {'degree': 4, 'field': [-1, -20, -4, 0, 1], 'lmfdb_label': '5070.t4', 'torsion': [4]}
  • id: 265681
    {'degree': 4, 'field': [9, 3, 4, -1, 1], 'lmfdb_label': '5070.t4', 'torsion': [2, 6]}
  • id: 265682
    {'degree': 6, 'field': [12, 12, -8, -9, 7, -3, 1], 'lmfdb_label': '5070.t4', 'torsion': [2, 6]}
  • id: 265685
    {'degree': 8, 'field': [39, 78, 23, -30, -24, 22, -7, -2, 1], 'lmfdb_label': '5070.t4', 'torsion': [12]}
  • id: 265683
    {'degree': 8, 'field': [1600, -3200, 3320, -1800, 554, -84, 5, -2, 1], 'lmfdb_label': '5070.t4', 'torsion': [2, 4]}
  • id: 265684
    {'degree': 8, 'field': [14400, 0, -828, 0, 96, 0, -3, 0, 1], 'lmfdb_label': '5070.t4', 'torsion': [2, 4]}
  • id: 265686
    {'degree': 12, 'field': [144, 144, 240, 120, 88, -132, 197, -99, 30, -3, 2, -3, 1], 'lmfdb_label': '5070.t4', 'torsion': [6, 6]}
  • id: 265687
    {'degree': 16, 'field': [-27315900, -102492000, -134733600, -68310000, -19397460, -19128000, -4296000, 4893000, 303901, -419752, -10120, 9008, 514, 232, -40, -8, 1], 'lmfdb_label': '5070.t4', 'torsion': [8]}
  • id: 265688
    {'degree': 16, 'field': [1521, 3042, 5187, 4134, 3805, 3912, -810, -916, 1046, -916, 302, -280, 117, -30, 11, -2, 1], 'lmfdb_label': '5070.t4', 'torsion': [2, 12]}
  • id: 265689
    {'degree': 16, 'field': [2304, -3456, 3744, -3024, 2004, -2160, 1254, -936, 469, -234, 314, -180, 201, -84, 26, -6, 1], 'lmfdb_label': '5070.t4', 'torsion': [2, 12]}
  • id: 265690
    {'degree': 18, 'field': [-123084, 715104, -684684, 401466, 397410, 287820, -94883, -83931, 26607, 24387, 25146, -4632, -11975, -1902, 1194, 135, -60, -3, 1], 'lmfdb_label': '5070.t4', '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: 98561
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '5070.t4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 98562
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '5070.t4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 98563
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '5070.t4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 98564
    {'conductor': 5070, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '5070.t4', '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: 1697129
    {'adelic_gens': [[1, 6, 6, 37], [1, 12, 0, 1], [11, 2, 1510, 1551], [110, 1557, 1107, 8], [781, 12, 6, 73], [266, 11, 1029, 1540], [1549, 12, 1548, 13], [937, 12, 942, 73], [1, 0, 12, 1], [75, 328, 38, 317]], 'adelic_image': '1560.96.1.?', 'conductor': 5070, 'lmfdb_label': '5070.t4', 'prime': 0}
  • id: 25230
    {'conductor': 5070, 'elladic_image': '2.3.0.1', 'lmfdb_label': '5070.t4', 'modell_image': '2B', 'prime': 2}
  • id: 25231
    {'conductor': 5070, 'elladic_image': '3.4.0.1', 'lmfdb_label': '5070.t4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 186953
    {'lmfdb_iso': '5070.t', 'p': 7, 'prec': 20, 'unit': 3001875681668267, 'val': 1}
  • id: 186949
    {'lmfdb_iso': '5070.t', 'p': 19, 'prec': 20, 'unit': 1091891723663312596168927, 'val': 1}
  • id: 186960
    {'lmfdb_iso': '5070.t', 'p': 23, 'prec': 20, 'unit': 28011437257356722240710081, 'val': 1}
  • id: 186963
    {'lmfdb_iso': '5070.t', 'p': 31, 'prec': 20, 'unit': 16459236687747061146033343846, 'val': 1}
  • id: 186952
    {'lmfdb_iso': '5070.t', 'p': 37, 'prec': 20, 'unit': 603309716207717824823724640338, 'val': 1}
  • id: 186954
    {'lmfdb_iso': '5070.t', 'p': 41, 'prec': 20, 'unit': 1566906848509027227330450671881, 'val': 1}
  • id: 186955
    {'lmfdb_iso': '5070.t', 'p': 43, 'prec': 20, 'unit': 6800451008407510737534923576117, 'val': 1}
  • id: 186958
    {'lmfdb_iso': '5070.t', 'p': 53, 'prec': 20, 'unit': 540273382089958791824012290760690, 'val': 1}
  • id: 186962
    {'lmfdb_iso': '5070.t', 'p': 61, 'prec': 20, 'unit': 6017595128013617339860777236650946, 'val': 1}
  • id: 186951
    {'lmfdb_iso': '5070.t', 'p': 67, 'prec': 20, 'unit': 44718316045581543801800292594894898, 'val': 1}
  • id: 186959
    {'lmfdb_iso': '5070.t', 'p': 73, 'prec': 20, 'unit': 170623390745126505647129719154862501, 'val': 1}
  • id: 186956
    {'lmfdb_iso': '5070.t', 'p': 79, 'prec': 20, 'unit': 1061317081908227891663867488167160154, 'val': 1}
  • id: 186957
    {'lmfdb_iso': '5070.t', 'p': 83, 'prec': 20, 'unit': 654356113947701951255456567210340211, 'val': 1}
  • id: 186961
    {'lmfdb_iso': '5070.t', 'p': 89, 'prec': 20, 'unit': 5691628397368479211740253844634259419, 'val': 1}
  • id: 186950
    {'lmfdb_iso': '5070.t', 'p': 97, 'prec': 20, 'unit': 37665324227797334657004048397348329447, 'val': 1}