Elliptic curve data - 7728.t1

Formats: - HTML - YAML - JSON - 2024-04-20T02:45:16.108204

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '7728p', 'Clabel': '7728p2', 'Cnumber': 2, 'abc_quality': 1.0627385135660905, 'absD': 406962030809972736, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1288, 'ainvs': [0, 1, 0, -4004232, -3085271820], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 7728, 'degree': 202752, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4426290472504540858214009386', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2], 'jinv': [1733490909744055732873, 99355964553216], 'lmfdb_iso': '7728.t', 'lmfdb_label': '7728.t1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -250264, 48082240], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '184.6.0.?', '1288.12.0.?'], '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': '1.6440997152216028571553632211', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7494818666905087764041688171', 'prec': 100}, 'szpiro_ratio': 6.391680182389995, '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, 2, 0, -1, 0, 1, 0, 4, 0, -4, 0, 2, 0, -4, 0, 2, 0], 'aplist': [0, 1, 2, -1, 4, -4, -4, 2, -1, -6, -6, -2, -10, -8, -10, -6, 12, -10, -8, 4, -2, 8, 6, 0, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 7728, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '7728.t', 'trace_hash': 1784658460338913222}
• 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': '0.0075571730455123049971501939463', 'prec': 110}, 'conductor': 7728, 'gens': [[4926, 311040, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6440997152216028571553632211', 'prec': 100}], 'lmfdb_label': '7728.t1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10672624536816712913070997143', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6149948677271836154629967265015574960', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-1149, 0, 1]], 'xcoord_integral_points': [-1149, 4926]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '7728.t1'}
• ec_torsion_growth •

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

  
  
  • id: 404343
    {'degree': 2, 'field': [-46, 0, 1], 'lmfdb_label': '7728.t1', 'torsion': [2, 2]}
  • id: 404344
    {'degree': 4, 'field': [11, 9, -2, -1, 1], 'lmfdb_label': '7728.t1', 'torsion': [4]}
  • id: 404347
    {'degree': 8, 'field': [-15552, 0, 720, 0, -432, 0, 0, 0, 1], 'lmfdb_label': '7728.t1', 'torsion': [6]}
  • id: 404345
    {'degree': 8, 'field': [81, 0, 108, 0, -2890, 0, 12, 0, 1], 'lmfdb_label': '7728.t1', 'torsion': [2, 4]}
  • id: 404346
    {'degree': 8, 'field': [441, 0, 1414, 0, -33, 0, -6, 0, 1], 'lmfdb_label': '7728.t1', 'torsion': [2, 4]}
  • id: 404348
    {'degree': 16, 'field': [7970908, 3203848, -3543800, -5330024, 5687864, 428512, -589848, -129440, 73439, 29522, -4158, -1582, 203, 98, -8, -4, 1], 'lmfdb_label': '7728.t1', 'torsion': [8]}
  • id: 404349
    {'degree': 16, 'field': [3830743449, 0, -90167836284, 0, -3396554532, 0, -150297364, 0, -5680402, 0, -18676, 0, 7084, 0, -92, 0, 1], 'lmfdb_label': '7728.t1', 'torsion': [2, 6]}
• 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: 159538
    {'conductor': 7728, 'conductor_valuation': 4, 'discriminant_valuation': 23, 'j_denominator_valuation': 11, 'kodaira_symbol': -19, 'lmfdb_label': '7728.t1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 159539
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '7728.t1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 159540
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '7728.t1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 159541
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7728.t1', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1715015
    {'adelic_gens': [[562, 1, 1007, 0], [1, 2, 2, 5], [2, 1, 643, 0], [1, 4, 0, 1], [1285, 4, 1284, 5], [1, 0, 4, 1], [185, 4, 370, 9], [3, 4, 8, 11], [484, 809, 161, 1128]], 'adelic_image': '1288.12.0.?', 'conductor': 7728, 'lmfdb_label': '7728.t1', 'prime': 0}
  • id: 37891
    {'conductor': 7728, 'elladic_image': '2.3.0.1', 'lmfdb_label': '7728.t1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 315397
    {'lmfdb_iso': '7728.t', 'p': 5, 'prec': 20, 'unit': 15460328454288, 'val': 1}
  • id: 315396
    {'lmfdb_iso': '7728.t', 'p': 11, 'prec': 20, 'unit': 13986493782952927506, 'val': 1}
  • id: 315403
    {'lmfdb_iso': '7728.t', 'p': 13, 'prec': 20, 'unit': 326447445186615498000, 'val': 1}
  • id: 315405
    {'lmfdb_iso': '7728.t', 'p': 17, 'prec': 20, 'unit': 206231754065505616455372, 'val': 1}
  • id: 315406
    {'lmfdb_iso': '7728.t', 'p': 19, 'prec': 20, 'unit': 1348952768790319348529922, 'val': 1}
  • id: 315402
    {'lmfdb_iso': '7728.t', 'p': 29, 'prec': 20, 'unit': 1155345162498207737772112619, 'val': 1}
  • id: 315399
    {'lmfdb_iso': '7728.t', 'p': 31, 'prec': 20, 'unit': 13296192584794997706348371787, 'val': 1}
  • id: 315413
    {'lmfdb_iso': '7728.t', 'p': 37, 'prec': 20, 'unit': 380094921393978744681198061283, 'val': 1}
  • id: 315400
    {'lmfdb_iso': '7728.t', 'p': 41, 'prec': 20, 'unit': 1069908067206920085877952561351, 'val': 1}
  • id: 315401
    {'lmfdb_iso': '7728.t', 'p': 43, 'prec': 20, 'unit': 5795814221977378412591812073781, 'val': 1}
  • id: 315411
    {'lmfdb_iso': '7728.t', 'p': 47, 'prec': 20, 'unit': 2216579546493301778523575103488, 'val': 1}
  • id: 315407
    {'lmfdb_iso': '7728.t', 'p': 53, 'prec': 20, 'unit': 118036285017422338593474762858485, 'val': 1}
  • id: 315408
    {'lmfdb_iso': '7728.t', 'p': 59, 'prec': 20, 'unit': 3000884874135045474909017236213750, 'val': 1}
  • id: 315412
    {'lmfdb_iso': '7728.t', 'p': 61, 'prec': 20, 'unit': 838883458110425724324949267822927, 'val': 1}
  • id: 315395
    {'lmfdb_iso': '7728.t', 'p': 67, 'prec': 20, 'unit': 17844044003971788571006404978792004, 'val': 1}
  • id: 315398
    {'lmfdb_iso': '7728.t', 'p': 71, 'prec': 20, 'unit': 128379816882834901977136563747675231, 'val': 1}
  • id: 315409
    {'lmfdb_iso': '7728.t', 'p': 73, 'prec': 20, 'unit': 121159542016295888518965307226015114, 'val': 1}
  • id: 315404
    {'lmfdb_iso': '7728.t', 'p': 79, 'prec': 20, 'unit': 456986266254565728645982213406535400, 'val': 1}
  • id: 315410
    {'lmfdb_iso': '7728.t', 'p': 83, 'prec': 20, 'unit': 1870469623412108119898478408467347252, 'val': 1}
  • id: 315394
    {'lmfdb_iso': '7728.t', 'p': 97, 'prec': 20, 'unit': 41912329771596765022864676458842120110, 'val': 1}