{
  "id": 174,
  "curve_key": "107312675580214936379749161:-1108736585358091967294760632848942653909",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-2235680741254477841244774",
    "1283259936757609808257953240813254080"
  ],
  "rank_lower_bound": 16,
  "naive_height": 179.81336702001462,
  "faltings_height": 12.794622466751935,
  "conductor": "145828484209869499295970073108577927976542470773736770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "31",
    "89",
    "109",
    "283291781381707777230208241994647890971677"
  ],
  "discriminant": "3771450175401594216284632730407117555621648825258951862297267210498122500",
  "regulator": "328235901585154.0624787348667814960685903389391649690219209571650604171",
  "points": [
    [
      "1286357640157919",
      "46136250466930114059212"
    ],
    [
      "341905934694529/9",
      "6317254430329285246819/27"
    ],
    [
      "12049952967584",
      "41521230102586140032"
    ],
    [
      "5541103781669",
      "12610637009143550369"
    ],
    [
      "1247207651143055/289",
      "41691156313706448253285/4913"
    ],
    [
      "2888647988814",
      "4350731104079225264"
    ],
    [
      "1530043997586",
      "1201854479511790052"
    ],
    [
      "30722339887386/25",
      "78231956856463548194/125"
    ],
    [
      "438561162327677816/395641",
      "101720666381642456845702348/248858189"
    ],
    [
      "944756146061",
      "119758896370184162"
    ],
    [
      "1432445502137738039/1592644",
      "-11759942951095767341832359/2009916728"
    ],
    [
      "370009504648442561/410881",
      "-4168265120033709582603338/263374721"
    ],
    [
      "909974167949",
      "-48529226780115823"
    ],
    [
      "4263622168043034/4489",
      "-38798376235741601969564/300763"
    ],
    [
      "988130760281",
      "-197302981196592103"
    ],
    [
      "1006411077788940806/755161",
      "537469664983254488916048808/656234909"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-110, 6, 60, 44, 94, -94] with shift t=2524/5: 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 16:01:32",
  "updated_at": "2026-07-01 22:39:39"
}