{
  "id": 3988,
  "curve_key": "3914690866515330079539116814899688221028718561:-170630106014014614161033865112459389800715644012752863563156773039441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-81556059719069376657064933643743504604764970",
    "197488548627331729353041658652962519450921684418438094943084756900"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "naive_height": 314.94319664927536,
  "faltings_height": 24.27419456939622,
  "conductor": "15662834656502411939691591195371771384959399565490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "29",
    "37",
    "43",
    "53",
    "59",
    "83",
    "107",
    "109",
    "127",
    "157",
    "269",
    "347",
    "607",
    "3181",
    "1307863",
    "23637023"
  ],
  "discriminant": "17868772826149492413880920722801078677204878195067534446780445312238425425762049894273464111586229241627824859966937063217412900000000",
  "regulator": "96401226198752026.355559829738262060691642321011532628117840365",
  "points": [
    [
      "-120243839912260957659297104/12321",
      "345750160067975373571358154414416131382/1367631"
    ],
    [
      "-9149881806292321788756944/1681",
      "47756914164329357832768619045499869622/68921"
    ],
    [
      "-9894134912029735099986933822669584421140/1052879890435813449",
      "395540011125440075111601861839739870240201612268539150849190/1080359378574418629790852293"
    ],
    [
      "-24618748843797520631413460/17161",
      "1254778192942578608982910260951296320730/2248091"
    ],
    [
      "34405472329478745822660306776114140/3024924471361",
      "4529688046080846164029387307614749620609577446500130/5261042413249663391"
    ],
    [
      "55239872304549819810969610/5329",
      "-265536992712536667944395299817543706390/389017"
    ],
    [
      "5432796162540409927662977201205940/26396175961",
      "400056724053577608363792017848071386799688745340670/4288560312207709"
    ],
    [
      "-35944524506507656143908971470343814837/4549359237327844",
      "-181180467181511079827903418405954538205573655648985130933/306849449138253035629672"
    ],
    [
      "24280430854176707767360492686484525/9498156920464",
      "-2211854875208229930370365989520410676251196457045885/29272445798433365312"
    ],
    [
      "5958350020709394158783059923057187660/486553467013849",
      "-10919794188130612066332454207937225348448069471811817810/10732375453592399646493"
    ],
    [
      "-10455797182038095222544549615854331148340/1095206155301034529",
      "-373099400945104803573566481209876749365601522302353983468210/1146156215662052384399814833"
    ],
    [
      "350569198934455966970128918194403612068358601553699309953563859518685813990346197802034622849442040/45462698592138874554109501744925311817756996850086265813145370092129400484921",
      "-1596219414013135361153929959436165225551413053066706904738545146935255967937114893999580669876663778347353041064702868865346424042800718206995182770/9693549151608346865941089511217369003021627158487330471590471507494674456853303380951023106451947660828233460396781"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3705 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 12: 12 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 04:40:24",
  "updated_at": "2026-10-05 04:40:24"
}