Elliptic curve data - 11760.p1

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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': '11760bq', 'Clabel': '11760bq7', 'Cnumber': 7, 'abc_quality': 1.0735374703334082, 'absD': 195165573120, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [0, -1, 0, -1693456, -847656704], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 11760, 'degree': 98304, 'elladic_images': ['16.48.0.121'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9569718635647034839435441175', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 16, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [1114544804970241, 405], 'lmfdb_iso': '11760.p', 'lmfdb_label': '11760.p1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -2160, -39540], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '10.6.0.a.1', '16.48.0.x.2', '20.12.0.g.1', '28.12.0-4.c.1.2', '40.48.0.bj.1', '56.48.0-8.bb.2.6', '80.96.1.?', '96.96.1.?', '112.96.0.?', '140.24.0.?', '160.192.5.?', '240.192.5.?', '280.96.0.?', '480.384.13.?', '560.192.1.?', '672.192.1.?', '1120.384.5.?', '1680.384.5.?', '3360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.3929520095534666291222985969', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 245], [3, 4, 3920], [5, 6, 2352], [7, 26, 240]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562432', 'prec': 103}, 'szpiro_ratio': 5.829894613549096, '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, 0, 0, 1, 0, 4, 0, 2, 0, 1, 0, -2, 0, 4, 0], 'aplist': [0, -1, -1, 0, 4, 2, -2, 4, 0, -2, 0, -10, -10, -4, 8, -10, -4, 2, -12, 8, -10, 0, 12, 6, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 11760, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '11760.p', 'trace_hash': 2046204327868987198}
• 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': '0.019961622434085081265774489126', 'prec': 107}, 'conductor': 11760, 'gens': [[2498, 102486, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '7.3929520095534666291222985969', 'prec': 100}], 'lmfdb_label': '11760.p1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.13234454769759057422974421892', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9136675594173874036326074793726911300', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-751, 0, 1]], 'xcoord_integral_points': [-751, 2498]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': 'a', '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': '11760.p1'}
• ec_torsion_growth •

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

  
  
  • id: 608126
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '11760.p1', 'torsion': [2, 2]}
  • id: 608128
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '11760.p1', 'torsion': [4]}
  • id: 608127
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '11760.p1', 'torsion': [4]}
  • id: 608129
    {'degree': 4, 'field': [4, 2, 5, -1, 1], 'lmfdb_label': '11760.p1', 'torsion': [2, 4]}
  • id: 608130
    {'degree': 4, 'field': [16, 0, 6, 0, 1], 'lmfdb_label': '11760.p1', 'torsion': [8]}
  • id: 608131
    {'degree': 4, 'field': [134, 16, -15, -2, 1], 'lmfdb_label': '11760.p1', 'torsion': [8]}
  • id: 608137
    {'degree': 8, 'field': [-7203, 0, 2401, 0, -294, 0, 0, 0, 1], 'lmfdb_label': '11760.p1', 'torsion': [6]}
  • id: 608133
    {'degree': 8, 'field': [21, 140, 212, -120, 29, -20, -2, 0, 1], 'lmfdb_label': '11760.p1', 'torsion': [8]}
  • id: 608132
    {'degree': 8, 'field': [81, -54, -270, -186, -61, 14, 0, -4, 1], 'lmfdb_label': '11760.p1', 'torsion': [2, 4]}
  • id: 608134
    {'degree': 8, 'field': [225, 0, 190, 0, 39, 0, -6, 0, 1], 'lmfdb_label': '11760.p1', 'torsion': [2, 8]}
  • id: 608135
    {'degree': 8, 'field': [39526, -2072, 5576, -6896, 3169, 332, -106, -4, 1], 'lmfdb_label': '11760.p1', 'torsion': [16]}
  • id: 608136
    {'degree': 8, 'field': [817846, 98728, -93784, -9776, 4609, 332, -106, -4, 1], 'lmfdb_label': '11760.p1', 'torsion': [16]}
  • id: 608140
    {'degree': 16, 'field': [-33939, 626292, -1699704, 2127708, -1732914, 1175256, -417816, 235524, -60413, 16544, -5696, -1204, -234, 28, 16, -8, 1], 'lmfdb_label': '11760.p1', 'torsion': [2, 8]}
  • id: 608138
    {'degree': 16, 'field': [441, 0, -1064, 0, 130, 0, 344, 0, 659, 0, 344, 0, 110, 0, 16, 0, 1], 'lmfdb_label': '11760.p1', 'torsion': [4, 4]}
  • id: 608139
    {'degree': 16, 'field': [2116, 0, 7752, 0, 16920, 0, 4692, 0, -1091, 0, -192, 0, 90, 0, -12, 0, 1], 'lmfdb_label': '11760.p1', 'torsion': [2, 8]}
  • id: 608145
    {'degree': 16, 'field': [2304, 0, -4032, 0, 3424, 0, -2016, 0, 669, 0, -63, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '11760.p1', 'torsion': [12]}
  • id: 608144
    {'degree': 16, 'field': [59049, 0, -15309, 0, 10935, 0, -3402, 0, 2535, 0, -182, 0, 102, 0, 0, 0, 1], 'lmfdb_label': '11760.p1', 'torsion': [12]}
  • id: 608141
    {'degree': 16, 'field': [4268002, 2980424, -1883764, -2012808, 557486, 531928, -165284, -12600, 7915, -6264, 4588, -2152, 662, -168, 44, -8, 1], 'lmfdb_label': '11760.p1', 'torsion': [16]}
  • id: 608143
    {'degree': 16, 'field': [18259949, 11353210, -2261918, -15864730, 2307095, 6273708, -1290254, -698032, 184850, -610, -6258, 3584, -658, 0, 20, -8, 1], 'lmfdb_label': '11760.p1', 'torsion': [2, 6]}
  • id: 608142
    {'degree': 16, 'field': [400908316, 133399616, -86333224, -85094256, 21153938, 22398016, -2290076, -3889488, 319363, 388296, -32084, -23008, 2318, 672, -76, -8, 1], 'lmfdb_label': '11760.p1', 'torsion': [2, 16]}
• 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: 253124
    {'conductor': 11760, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '11760.p1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 253125
    {'conductor': 11760, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '11760.p1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 253126
    {'conductor': 11760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '11760.p1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 253127
    {'conductor': 11760, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '11760.p1', 'prime': 7, 'reduction_type': 0, '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: 1742044
    {'adelic_gens': [[1889, 448, 1050, 3359], [1, 0, 32, 1], [1, 32, 0, 1], [1439, 0, 0, 3359], [5, 28, 68, 381], [421, 2912, 1876, 2913], [1303, 1946, 1302, 491], [3329, 32, 3328, 33], [1072, 2905, 1463, 3186], [23, 18, 798, 1355]], 'adelic_image': '3360.768.13.?', 'conductor': 11760, 'lmfdb_label': '11760.p1', 'prime': 0}
  • id: 56394
    {'conductor': 11760, 'elladic_image': '16.48.0.121', 'lmfdb_label': '11760.p1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 510724
    {'lmfdb_iso': '11760.p', 'p': 11, 'prec': 20, 'unit': 47564156107934591032, 'val': 1}
  • id: 510730
    {'lmfdb_iso': '11760.p', 'p': 13, 'prec': 20, 'unit': 542441208304030642966, 'val': 1}
  • id: 510732
    {'lmfdb_iso': '11760.p', 'p': 17, 'prec': 20, 'unit': 166821322999378978994368, 'val': 1}
  • id: 510733
    {'lmfdb_iso': '11760.p', 'p': 19, 'prec': 20, 'unit': 755418282368066728973146, 'val': 1}
  • id: 510729
    {'lmfdb_iso': '11760.p', 'p': 29, 'prec': 20, 'unit': 4026900816166522239513868725, 'val': 1}
  • id: 510725
    {'lmfdb_iso': '11760.p', 'p': 37, 'prec': 20, 'unit': 156216359198064219727466798901, 'val': 1}
  • id: 510727
    {'lmfdb_iso': '11760.p', 'p': 41, 'prec': 20, 'unit': 2389237624522883644616149878979, 'val': 1}
  • id: 510728
    {'lmfdb_iso': '11760.p', 'p': 43, 'prec': 20, 'unit': 6076807448115637548957183446350, 'val': 1}
  • id: 510731
    {'lmfdb_iso': '11760.p', 'p': 47, 'prec': 20, 'unit': 35732876459739765762671318706115, 'val': 1}
  • id: 510734
    {'lmfdb_iso': '11760.p', 'p': 53, 'prec': 20, 'unit': 240861638957688572807678255506913, 'val': 1}
  • id: 510738
    {'lmfdb_iso': '11760.p', 'p': 59, 'prec': 20, 'unit': 1540372091576097128237128090982094, 'val': 1}
  • id: 510739
    {'lmfdb_iso': '11760.p', 'p': 61, 'prec': 20, 'unit': 2050697979245915401875838713681354, 'val': 1}
  • id: 510723
    {'lmfdb_iso': '11760.p', 'p': 67, 'prec': 20, 'unit': 10930841899750472959503513087319888, 'val': 1}
  • id: 510726
    {'lmfdb_iso': '11760.p', 'p': 71, 'prec': 20, 'unit': 26263080777817718093039525050480200, 'val': 1}
  • id: 510735
    {'lmfdb_iso': '11760.p', 'p': 73, 'prec': 20, 'unit': 139634526776626078014679010297466122, 'val': 1}
  • id: 510736
    {'lmfdb_iso': '11760.p', 'p': 83, 'prec': 20, 'unit': 1708978465868416793468128480470537008, 'val': 1}
  • id: 510737
    {'lmfdb_iso': '11760.p', 'p': 89, 'prec': 20, 'unit': 5511055059698909600645466922042310472, 'val': 1}
  • id: 510722
    {'lmfdb_iso': '11760.p', 'p': 97, 'prec': 20, 'unit': 41438261258572961973680362216188782386, 'val': 1}