Elliptic curve data - 735.c8

Formats: - HTML - YAML - JSON - 2025-11-08T03:50:10.642863

• 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': '735e', 'Clabel': '735e6', 'Cnumber': 6, 'abc_quality': 1.0558519748642754, 'absD': 413609765625, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [1, 0, 0, 1714, 14685], 'analytic_rank': 1, 'bad_primes': [3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 735, 'degree': 768, 'elladic_images': ['8.48.0.197'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.91725109272478551981769593529', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4733169839, 3515625], 'lmfdb_iso': '735.c', 'lmfdb_label': '735.c8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 35, -28], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0.n.2', '24.96.1.cv.2', '28.24.0-4.d.1.1', '56.96.0-8.n.2.4', '80.96.1.?', '160.192.5.?', '168.192.1.?', '240.192.5.?', '480.384.13.?', '560.192.1.?', '1120.384.5.?', '1680.384.5.?', '3360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3783561536481783106269485771', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 245], [5, 6, 147], [7, 26, 15]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436432', 'prec': 110}, 'szpiro_ratio': 5.144543649699505, '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, 0, 3, 1, 1, -4, -1, 2, 0, -1, -1, -2, -1, -4, 1], 'aplist': [-1, 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': 735, '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': '735.c', 'trace_hash': 2064110924542206652}
• 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': '0.15969297947268065012619591301', 'prec': 103}, 'conductor': 735, 'gens': [[4, 145, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3783561536481783106269485771', 'prec': 100}], 'lmfdb_label': '735.c8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.60332285028311738063655998945', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6631875266485868389615839320591057643', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-33, 33, 2]], 'xcoord_integral_points': [4, 148]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 1], '3': [2, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [3, 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': '735.c8'}
• ec_torsion_growth •

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

  
  
  • id: 34515
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [4]}
  • id: 34514
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [2, 2]}
  • id: 34516
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '735.c8', 'torsion': [8]}
  • id: 34517
    {'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [2, 8]}
  • id: 34518
    {'degree': 4, 'field': [81, 0, -24, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [8]}
  • id: 34519
    {'degree': 4, 'field': [81, 0, 24, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [8]}
  • id: 34522
    {'degree': 8, 'field': [-45, 117, -123, -30, 15, -1, -3, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [6]}
  • id: 34521
    {'degree': 8, 'field': [79, -314, 314, -2, 7, -10, 8, -4, 1], 'lmfdb_label': '735.c8', 'torsion': [16]}
  • id: 34520
    {'degree': 8, 'field': [106, 148, -106, -92, 67, -28, 14, -4, 1], 'lmfdb_label': '735.c8', 'torsion': [4, 8]}
  • id: 34525
    {'degree': 16, 'field': [-2581094, -8353800, -11227148, -5682360, 2360230, 4426800, 2140492, 97440, -418661, -188520, -9332, 13080, 2590, -240, -92, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [16]}
  • id: 34528
    {'degree': 16, 'field': [225, 0, 468, 0, 360, 0, -1369, 0, 872, 0, -295, 0, 85, 0, -14, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [12]}
  • id: 34529
    {'degree': 16, 'field': [256, -512, 1280, -1184, 1344, -536, 324, -56, -281, 216, 28, -47, 32, -21, 11, -4, 1], 'lmfdb_label': '735.c8', 'torsion': [24]}
  • id: 34524
    {'degree': 16, 'field': [256, 0, 0, 0, 48, 0, 0, 0, 113, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [2, 16]}
  • id: 34523
    {'degree': 16, 'field': [676, -1872, 1064, -2432, 11910, 168, 4152, -4082, 969, -1446, 598, -282, 164, -50, 22, -4, 1], 'lmfdb_label': '735.c8', 'torsion': [2, 16]}
  • id: 34527
    {'degree': 16, 'field': [2025, 0, 2619, 0, 20799, 0, 4086, 0, 813, 0, 337, 0, 39, 0, 6, 0, 1], 'lmfdb_label': '735.c8', 'torsion': [2, 6]}
  • id: 34526
    {'degree': 16, 'field': [6241, 0, -541544, 0, 15386776, 0, 2051056, 0, 136174, 0, -37016, 0, 2488, 0, -80, 0, 1], 'lmfdb_label': '735.c8', '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: 9307
    {'conductor': 735, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '735.c8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9308
    {'conductor': 735, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '735.c8', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9309
    {'conductor': 735, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '735.c8', '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: 1669324
    {'adelic_gens': [[2017, 2408, 0, 1], [1, 0, 32, 1], [25, 16, 1624, 2249], [1, 32, 0, 1], [1439, 0, 0, 3359], [1625, 2912, 182, 2409], [967, 1456, 3255, 3193], [3329, 32, 3328, 33], [1933, 1456, 1694, 2745], [1, 32, 4, 129]], 'adelic_image': '3360.768.13.?', 'conductor': 735, 'lmfdb_label': '735.c8', 'prime': 0}
  • id: 3367
    {'conductor': 735, 'elladic_image': '8.48.0.197', 'lmfdb_label': '735.c8', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 14177
    {'lmfdb_iso': '735.c', 'p': 11, 'prec': 20, 'unit': 30738200652453025288, 'val': 1}
  • id: 14183
    {'lmfdb_iso': '735.c', 'p': 13, 'prec': 20, 'unit': 1146388746085532978987, 'val': 1}
  • id: 14185
    {'lmfdb_iso': '735.c', 'p': 17, 'prec': 20, 'unit': 18898037352432526247186, 'val': 1}
  • id: 14186
    {'lmfdb_iso': '735.c', 'p': 19, 'prec': 20, 'unit': 27038681665803651874367, 'val': 2}
  • id: 14182
    {'lmfdb_iso': '735.c', 'p': 29, 'prec': 20, 'unit': 3951301329668530486944564196, 'val': 1}
  • id: 14178
    {'lmfdb_iso': '735.c', 'p': 37, 'prec': 20, 'unit': 85465324003400387928540876769, 'val': 1}
  • id: 14180
    {'lmfdb_iso': '735.c', 'p': 41, 'prec': 20, 'unit': 3858637450293731347121118400828, 'val': 1}
  • id: 14181
    {'lmfdb_iso': '735.c', 'p': 43, 'prec': 20, 'unit': 2100942341093264782282970108530, 'val': 1}
  • id: 14184
    {'lmfdb_iso': '735.c', 'p': 47, 'prec': 20, 'unit': 55725550706223056815915222427997, 'val': 1}
  • id: 14187
    {'lmfdb_iso': '735.c', 'p': 53, 'prec': 20, 'unit': 416815240279246088518009176124978, 'val': 1}
  • id: 14191
    {'lmfdb_iso': '735.c', 'p': 59, 'prec': 20, 'unit': 2271749289108195296263511589825069, 'val': 1}
  • id: 14192
    {'lmfdb_iso': '735.c', 'p': 61, 'prec': 20, 'unit': 3462542915683562123815889085956761, 'val': 1}
  • id: 14176
    {'lmfdb_iso': '735.c', 'p': 67, 'prec': 20, 'unit': 17296173740846638568505873155424350, 'val': 1}
  • id: 14179
    {'lmfdb_iso': '735.c', 'p': 71, 'prec': 20, 'unit': 82664792528213226086222032996985668, 'val': 1}
  • id: 14188
    {'lmfdb_iso': '735.c', 'p': 73, 'prec': 20, 'unit': 139406185722691119785143708710328927, 'val': 1}
  • id: 14189
    {'lmfdb_iso': '735.c', 'p': 83, 'prec': 20, 'unit': 1577857621044230306470216904459778931, 'val': 1}
  • id: 14190
    {'lmfdb_iso': '735.c', 'p': 89, 'prec': 20, 'unit': 8158418029879841332830891323564834929, 'val': 1}
  • id: 14175
    {'lmfdb_iso': '735.c', 'p': 97, 'prec': 20, 'unit': 48578377160727638045532225784942236494, 'val': 1}