{
  "id": 3976,
  "curve_key": "46969625398227530247159565279071321:5033514407979442491804890294233289838916712427316131",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-978533862463073546815824276647319",
    "-5825826861087317454214787039594217276271607258675"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 239.50442758040845,
  "faltings_height": 18.010094503055672,
  "conductor": "38689313102431608020253080619974416595190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "23",
    "37",
    "113",
    "139",
    "211",
    "281",
    "313",
    "431",
    "547",
    "2029",
    "3919",
    "133319",
    "364943"
  ],
  "discriminant": "45304149467366972609069043778706862859891739649150272251036561230001654669539751780208940822362250000",
  "regulator": "111018110862519451.660588693018186992864675730123786685921856",
  "points": [
    [
      "4287477770213909005729896329/28861932544",
      "274188796430468155565769448237671541617749/4903295996035072"
    ],
    [
      "-34023926040963483726538919831369/1260659774304441",
      "43046912097990714801747659279780091596078286662/44760697255365166429011"
    ],
    [
      "-425939181099764684405424187254/52318618051921",
      "478838111455908094075546642926535942484505457/378428987667050952281"
    ],
    [
      "-55179383261338813255895425/8512092121",
      "388784526006554251597700523966518531770/785334131175581"
    ],
    [
      "-20532701055641983527850/919681",
      "-1950852842203966960805604698531765/881974079"
    ],
    [
      "1596198668164577306854582957079/6244936026169",
      "2001135169879988920225650727513438422269329501/15606013945227990803"
    ],
    [
      "-16488415577637983647150929/2098464481",
      "-112834488210175081679838710046005688257/96128559410129"
    ],
    [
      "-2769184403528955810269206/445336609",
      "-1276338995570793079406642371406735341/9397938459727"
    ],
    [
      "176369742972291943480024798271159/4261327343418649",
      "-1378936493625006706182125561938996647697619277331/278174518622633071343107"
    ],
    [
      "1247015834694188737193946689078839/26372479329147249",
      "31362715923454357464876950775826272805955964274511/4282786656367518409997193"
    ],
    [
      "3122985219344036401956145361227896135071/53802306176946508166881",
      "143893213275922446226940586398338507319561025143889533248318/12479619310332089970464813243231279"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3703 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 11: 11 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:37:57",
  "updated_at": "2026-10-05 04:37:57"
}