Elliptic curve data - 11760.bx4

Formats: - HTML - YAML - JSON - 2025-10-02T14:26:41.496320

• 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': '11760ch', 'Clabel': '11760ch4', 'Cnumber': 4, 'abc_quality': 1.0358020223701003, 'absD': 58082632912900915200, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [0, 1, 0, -11814896, 15622984404], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 11760, 'degree': 589824, 'elladic_images': ['16.96.0.115'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7673844914232196995057146191', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 49, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [378499465220294881, 120530818800], 'lmfdb_iso': '11760.bx', 'lmfdb_label': '11760.bx4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -15070, 710612], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.48.0-8.bb.1.8', '16.96.0-16.v.1.12', '28.24.0-28.h.1.2', '56.96.0-56.bl.2.3', '80.192.2.?', '96.192.1.?', '112.192.1.?', '480.384.5.?', '560.384.5.?', '672.384.5.?', '3360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 3920], [5, 6, 2352], [7, 32, 240]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1012822363356177375358061259', 'prec': 100}, 'szpiro_ratio': 6.451691779841572, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 8, -2, 0, 6, 6, 4, 0, -10, 12, -14, 12, 8, -10, -16, -12, -10, -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.bx', 'trace_hash': 1274942468229796285}
• 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': '0.0039471203831846374569208723854', 'prec': 110}, 'conductor': 11760, 'gens': [], 'heights': [], 'lmfdb_label': '11760.bx4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.19388311473740156325473906475', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1021298357984250120758250360275824252', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[1444, 39690, 1]], 'xcoord_integral_points': [1444, 2011]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [0, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '11760.bx4'}
• ec_torsion_growth •

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

  
  
  • id: 608645
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '11760.bx4', 'torsion': [2, 8]}
  • id: 608647
    {'degree': 4, 'field': [9, 0, -34, 0, 1], 'lmfdb_label': '11760.bx4', 'torsion': [2, 16]}
  • id: 608646
    {'degree': 4, 'field': [700, 0, 0, 0, 1], 'lmfdb_label': '11760.bx4', 'torsion': [8]}
  • id: 608650
    {'degree': 8, 'field': [-327, 30, 492, -20, -304, 58, 22, -4, 1], 'lmfdb_label': '11760.bx4', 'torsion': [12]}
  • id: 608649
    {'degree': 8, 'field': [1, -2, 2, 4, -1, 4, 2, -2, 1], 'lmfdb_label': '11760.bx4', 'torsion': [2, 16]}
  • id: 608648
    {'degree': 8, 'field': [30276, 0, 2104, 0, -344, 0, 4, 0, 1], 'lmfdb_label': '11760.bx4', 'torsion': [4, 8]}
  • id: 608651
    {'degree': 16, 'field': [6561, 66096, 332928, -173220, 40306, -21652, 23240, -21064, 8931, 436, 280, -272, 126, 20, 8, -4, 1], 'lmfdb_label': '11760.bx4', 'torsion': [4, 16]}
  • id: 608655
    {'degree': 16, 'field': [3111696, 0, -3556224, 0, 1016064, 0, -140287, 0, 50666, 0, 1673, 0, 49, 0, -14, 0, 1], 'lmfdb_label': '11760.bx4', 'torsion': [2, 24]}
  • id: 608654
    {'degree': 16, 'field': [65610000, 0, -14580000, 0, -648000, 0, 945000, 0, 223425, 0, 10500, 0, -80, 0, -20, 0, 1], 'lmfdb_label': '11760.bx4', 'torsion': [2, 32]}
  • id: 608653
    {'degree': 16, 'field': [1001458116, 1100473920, -1782229152, -3134876640, -714871112, 1272255600, 997568976, 249916800, -4955400, -12608400, -1376384, 183120, 34548, -840, -312, 0, 1], 'lmfdb_label': '11760.bx4', 'torsion': [2, 32]}
  • id: 608652
    {'degree': 16, 'field': [1176490000, 0, 0, 0, 0, 0, 0, 0, 1166200, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '11760.bx4', 'torsion': [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: 253296
    {'conductor': 11760, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '11760.bx4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 253297
    {'conductor': 11760, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '11760.bx4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 253298
    {'conductor': 11760, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '11760.bx4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 253299
    {'conductor': 11760, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '11760.bx4', 'prime': 7, '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: 1741948
    {'adelic_gens': [[1121, 32, 1136, 513], [1, 0, 32, 1], [1, 32, 0, 1], [5, 28, 68, 381], [2121, 32, 1804, 2909], [3118, 3341, 2385, 1042], [2711, 26, 2118, 875], [2368, 3331, 2453, 798], [3329, 32, 3328, 33], [23, 18, 798, 1355]], 'adelic_image': '3360.768.13.?', 'conductor': 11760, 'lmfdb_label': '11760.bx4', 'prime': 0}
  • id: 56289
    {'conductor': 11760, 'elladic_image': '16.96.0.115', 'lmfdb_label': '11760.bx4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 11760.bx does not appear in ec_padic