Elliptic curve data - 87360.ds1

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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': '87360bj', 'Clabel': '87360bj5', 'Cnumber': 5, 'abc_quality': 1.0164587515547243, 'absD': 476338716672000000000, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 32760, 'ainvs': [0, -1, 0, -54545505, -155033545503], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 87360, 'degree': 8957952, 'elladic_images': ['2.3.0.1', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0729826677946302955681166301', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 9, 'iso_nlabel': 96, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [68463752473882049153689, 1817088000000000], 'lmfdb_iso': '87360.ds', 'lmfdb_label': '87360.ds1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -852274, -302906428], 'min_quad_twist_disc': 8, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '9.12.0.a.1', '18.36.0.a.1', '24.24.0-6.a.1.3', '72.72.0.?', '104.6.0.?', '156.24.0.?', '210.24.0.?', '312.48.0.?', '468.72.0.?', '630.72.1.?', '819.36.0.?', '840.48.0.?', '936.144.1.?', '1638.108.2.?', '2520.144.1.?', '3276.216.2.?', '5460.48.0.?', '6552.432.7.?', '8190.216.7.?', '10920.96.1.?', '16380.432.7.?', '32760.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.3762920266333600824857562962', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 105], [3, 4, 5824], [5, 6, 17472], [7, 8, 12480], [13, 14, 6720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.0332618969547123314422684479', 'prec': 100}, 'szpiro_ratio': 5.7179139963583, '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, -1, 0, 1, 0, 1, 0, 1, 0, 6, 0, -1, 0, -1, 0, 6, 0, -2, 0], 'aplist': [0, -1, 1, 1, 6, -1, 6, -2, 0, 0, -4, -2, -6, -8, 0, 6, -12, -8, -14, 12, 2, 8, 6, -6, -10], 'class_deg': 18, 'class_size': 6, 'conductor': 87360, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '87360.ds', 'trace_hash': 555516377760659917}
• 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': '0.0021421070413432770975326235245', 'prec': 110}, 'conductor': 87360, 'gens': [[-1880441, 17459000, 21]], 'heights': [{'__RealLiteral__': 0, 'data': '7.3762920266333600824857562962', 'prec': 100}], 'lmfdb_label': '87360.ds1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.055553382083886148419416423343', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.3760034477219471780661212127621019636', 'prec': 130}, 'tamagawa_product': 72, 'torsion_generators': [[-4247, 0, 1]], 'xcoord_integral_points': [-4247]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [5, 2], '5': [2, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 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': '87360.ds1'}
• ec_torsion_growth •

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

  
  
  • id: 4091133
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '87360.ds1', 'torsion': [2, 2]}
  • id: 4091134
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [6]}
  • id: 4091135
    {'degree': 4, 'field': [90, -52, 42, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [4]}
  • id: 4091136
    {'degree': 4, 'field': [256, 0, 38, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [2, 6]}
  • id: 4091138
    {'degree': 6, 'field': [997030, 423696, 74637, -1456, -528, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [18]}
  • id: 4091137
    {'degree': 6, 'field': [12595393, -42588, 12, -7098, -6, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [6]}
  • id: 4091141
    {'degree': 8, 'field': [400, 960, -320, -1328, 785, -148, 54, -4, 1], 'lmfdb_label': '87360.ds1', 'torsion': [12]}
  • id: 4091140
    {'degree': 8, 'field': [38970, 105300, 64626, -13104, 2539, -468, -14, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [2, 4]}
  • id: 4091139
    {'degree': 8, 'field': [57430, 111200, 66965, 12470, -1499, -548, -1, -2, 1], 'lmfdb_label': '87360.ds1', 'torsion': [2, 4]}
  • id: 4091143
    {'degree': 12, 'field': [12548281, -4844088, 581640, -823764, 135204, 5472, 19934, 0, 60, -228, -12, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [18]}
  • id: 4091144
    {'degree': 12, 'field': [196796042689, 0, -53235192, 0, -26617260, 0, -887410, 0, 60, 0, -12, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [2, 6]}
  • id: 4091142
    {'degree': 12, 'field': [1481855809225, 27915467580, 189899988, 275184, -36519114, -45864, 2434670, -45864, 24, 0, 6, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [3, 6]}
  • id: 4091145
    {'degree': 12, 'field': [3921686185600, 2038421767200, 562649054790, 66413066720, 2138991969, -693760704, -67781860, 2384928, 390030, -2912, -978, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [2, 18]}
  • id: 4091147
    {'degree': 16, 'field': [1218816, 0, 26383680, 0, 21203556, 0, 1251300, 0, 916681, 0, 36640, 0, -1374, 0, -20, 0, 1], 'lmfdb_label': '87360.ds1', 'torsion': [2, 12]}
  • id: 4091148
    {'degree': 16, 'field': [1777351720, 270318640, -194518776, -184700464, 62206668, 10763568, -909416, -815296, -25410, 23164, 14650, -3636, 771, 28, 42, -4, 1], 'lmfdb_label': '87360.ds1', 'torsion': [2, 12]}
  • id: 4091146
    {'degree': 16, 'field': [46122654852225, 56211092477400, 25479741947240, 4794279821800, 157719544530, -85060611880, -16434478008, -1320655656, 29637346, 14939448, 1302896, 112680, 2514, -328, 0, -8, 1], 'lmfdb_label': '87360.ds1', 'torsion': [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: 2133197
    {'conductor': 87360, 'conductor_valuation': 6, 'discriminant_valuation': 36, 'j_denominator_valuation': 18, 'kodaira_symbol': -30, 'lmfdb_label': '87360.ds1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2133198
    {'conductor': 87360, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '87360.ds1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2133199
    {'conductor': 87360, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '87360.ds1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 2133200
    {'conductor': 87360, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '87360.ds1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2133201
    {'conductor': 87360, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '87360.ds1', 'prime': 13, '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: 2239583
    {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [26236, 27, 13413, 298], [32725, 36, 32724, 37], [16379, 32724, 32750, 32399], [8191, 36, 0, 1], [19, 36, 3240, 6139], [10111, 36, 32066, 5047], [4696, 9, 7607, 31774], [1, 18, 14, 253], [29152, 27, 27589, 7922]], 'adelic_image': '32760.864.21.?', 'conductor': 87360, 'lmfdb_label': '87360.ds1', 'prime': 0}
  • id: 355947
    {'conductor': 87360, 'elladic_image': '2.3.0.1', 'lmfdb_label': '87360.ds1', 'modell_image': '2B', 'prime': 2}
  • id: 355948
    {'conductor': 87360, 'elladic_image': '9.12.0.1', 'lmfdb_label': '87360.ds1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 4516738
    {'lmfdb_iso': '87360.ds', 'p': 11, 'prec': 20, 'unit': 6708916560925055360, 'val': 1}
  • id: 4516739
    {'lmfdb_iso': '87360.ds', 'p': 17, 'prec': 20, 'unit': 189805388109250271053767, 'val': 1}
  • id: 4516740
    {'lmfdb_iso': '87360.ds', 'p': 19, 'prec': 20, 'unit': 343218940664931439995719, 'val': 1}
  • id: 4516746
    {'lmfdb_iso': '87360.ds', 'p': 31, 'prec': 20, 'unit': 10579611268931941829728025089, 'val': 1}
  • id: 4516733
    {'lmfdb_iso': '87360.ds', 'p': 37, 'prec': 20, 'unit': 216522376644510340948392926288, 'val': 1}
  • id: 4516735
    {'lmfdb_iso': '87360.ds', 'p': 41, 'prec': 20, 'unit': 2199200460613746154400018994244, 'val': 1}
  • id: 4516736
    {'lmfdb_iso': '87360.ds', 'p': 43, 'prec': 20, 'unit': 4341568836874358699242021646116, 'val': 1}
  • id: 4516741
    {'lmfdb_iso': '87360.ds', 'p': 53, 'prec': 20, 'unit': 162705635080667998392672146310117, 'val': 1}
  • id: 4516744
    {'lmfdb_iso': '87360.ds', 'p': 59, 'prec': 20, 'unit': 3281748401615034746461002494955061, 'val': 1}
  • id: 4516745
    {'lmfdb_iso': '87360.ds', 'p': 61, 'prec': 20, 'unit': 6745106968480927610092031599059886, 'val': 1}
  • id: 4516732
    {'lmfdb_iso': '87360.ds', 'p': 67, 'prec': 20, 'unit': 36418639207526473680795146857463326, 'val': 1}
  • id: 4516734
    {'lmfdb_iso': '87360.ds', 'p': 71, 'prec': 20, 'unit': 98712848726906930865504181359611558, 'val': 1}
  • id: 4516742
    {'lmfdb_iso': '87360.ds', 'p': 73, 'prec': 20, 'unit': 219688746591741778236189897896330017, 'val': 1}
  • id: 4516737
    {'lmfdb_iso': '87360.ds', 'p': 79, 'prec': 20, 'unit': 111784751740181079804727502200693112, 'val': 1}
  • id: 4516731
    {'lmfdb_iso': '87360.ds', 'p': 83, 'prec': 20, 'unit': 1550577572155018468603114564835149357, 'val': 1}
  • id: 4516743
    {'lmfdb_iso': '87360.ds', 'p': 89, 'prec': 20, 'unit': 9346288083611323554406564065204667554, 'val': 1}
  • id: 4516730
    {'lmfdb_iso': '87360.ds', 'p': 97, 'prec': 20, 'unit': 14110181460110492203382110828361260726, 'val': 1}