{
  "id": 182,
  "curve_key": "33868439134455088165022684851681:-197051210250681199142764101862645154541055843921",
  "ainvs": [
    "1",
    "0",
    "0",
    "-705592481967814336771305934410",
    "228068530382732810578825694652792716443320100"
  ],
  "rank_lower_bound": 16,
  "naive_height": 217.80010911472627,
  "faltings_height": 15.876700155877355,
  "conductor": "15495342387615096338864350597570025083525109638868085907030",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "31",
    "157",
    "2520531720283",
    "36758332594990127793731213603179"
  ],
  "discriminant": "11765406596767129399549312051539530956680847347822041839788385072806810895769600000000000",
  "regulator": "398172387122838.1436246285395286883159166095411598056198651333868740662",
  "points": [
    [
      "85806452822380243564820/151321",
      "25135032253556314427798345617442510/58863869"
    ],
    [
      "143543240122282594/9",
      "54310424664781703112741884/27"
    ],
    [
      "21932292098978439904820/3568321",
      "3219209126882113291254038149097510/6740558369"
    ],
    [
      "130893338118852930/361",
      "-30597161802530398523394340/6859"
    ],
    [
      "414053988634420",
      "-2626948398704820269210"
    ],
    [
      "478311460656900",
      "-67395889520080308010"
    ],
    [
      "20822298416231551497220/43943641",
      "100561680095391510410886047503310/291302396189"
    ],
    [
      "995281150564688360980/1907161",
      "-3697510664774461251644234425970/2633789341"
    ],
    [
      "474209115686009700/841",
      "-75118812688062079506219410/24389"
    ],
    [
      "775816978888420",
      "-12149729763811122725210"
    ],
    [
      "23783724072221805/16",
      "-3176744871249302298563455/64"
    ],
    [
      "7460889361050978666716020/26224641",
      "-20379053492046522649000488415619494810/134296386561"
    ],
    [
      "1753748568441128308/1089",
      "2054491546835926432213605734/35937"
    ],
    [
      "4980692083756696180/7569",
      "-4595470418622623132327656630/658503"
    ],
    [
      "467596474010420",
      "-611791578487052205210"
    ],
    [
      "3097490471898420",
      "-166616961664972326125210"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[348, -600, -216, 492, 876, -900] with shift t=389/10: let p6(x)=∏(x−a_i) and q(x)=p6(x−t)·p6(x+t); completing q to g(x)²−r(x) gives the genus-1 quartic model y²=r(x), whose x=a_i±t base points plus a few small-x extra points supply 16 independent rational points. The shift t was selected by a Nagao–Mestre prime-sum sieve; the witness points were found by an integer quartic-point search and certified independent via the Néron–Tate height-pairing matrix.",
  "created_at": "2026-06-25 16:02:11",
  "updated_at": "2026-07-01 22:41:37"
}