{
  "id": 409,
  "curve_key": "21344457421444531158171057321:-2849272083488567791277087543741099312014869",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-444676196280094399128563694",
    "3297768615148916483027180606633461900200"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 195.6917688337727,
  "faltings_height": 14.274089955226035,
  "conductor": "1809463015179380326823429025654865736412846312311714243982491941376610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "29",
    "47",
    "373",
    "36155150945461",
    "3658146940752362853285480075388737842001390989"
  ],
  "discriminant": "929329653164922471094982358455833192285812408593237768025722638184893743642937500",
  "regulator": "81900342214563417833.543127474364635229281229339928789603160691714507845811",
  "points": [
    [
      "-23821969611234",
      "19292279201517010092"
    ],
    [
      "193596845456411541/12769",
      "-9238406465636915675074902/1442897"
    ],
    [
      "-34733987926513258649/3538161",
      "545450958953350121329537546772/6655280841"
    ],
    [
      "1819330663103556/121",
      "4399702735070284506012/1331"
    ],
    [
      "200378240327380955859/3829849",
      "-2631308118957295461517157749719/7495014493"
    ],
    [
      "2956322830396491901/63001",
      "4630831126884244273150923022/15813251"
    ],
    [
      "1583311003995846510159/78198649",
      "-35224420629098416522803678391956/691510653107"
    ],
    [
      "-993421639266789/961",
      "-1825860788461954312210173/29791"
    ],
    [
      "427677231953043451746/22174681",
      "-4546388911536769746155696630082/104420572829"
    ],
    [
      "-21103176768966",
      "57303364409961390054"
    ],
    [
      "477019281514227331969/2985984",
      "-10331554847855041292836560929441/5159780352"
    ],
    [
      "-186145719720300831/142129",
      "3336745316937228619070544246/53582633"
    ],
    [
      "2248390547695411573281/47665216",
      "-97220356584163634901858190965237/329080651264"
    ],
    [
      "8075162436474904855494/17952169",
      "-724864847724571257861062902779234/76063340053"
    ],
    [
      "5765547517132050",
      "-437782034687446204684200"
    ],
    [
      "22793168168284175185254/149255089",
      "-3409820466005214264595759014424044/1823449422313"
    ],
    [
      "237208828931867456919/7579009",
      "2953636698279764083383192264309/20865011777"
    ],
    [
      "435507017681691",
      "9078032059655153293917"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "commentary": "Rank-18 curve from Mestre's quartic construction, specialized at T = 2539/5. The sextuple is [0, 113, 550, 753, 868, 1058], the canonical primitive representative from u = -3, v = -1/2 in the Mestre-Fermigier family, whose generic member has rank 12.",
  "created_at": "2026-08-28 20:29:24",
  "updated_at": "2026-08-28 20:29:24"
}