{
  "id": 6388,
  "curve_key": "19073504354530102203624885444688:-83268450694755109157286436471918768256448109120",
  "ainvs": [
    "0",
    "1",
    "0",
    "-397364674052710462575518446764",
    "96375521637447910551227209827899938086962316"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 216.0775588657292,
  "faltings_height": 15.745769361365731,
  "conductor": "4197634793865504992224501919470975981296",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "29",
    "67",
    "97",
    "101",
    "173",
    "191",
    "467",
    "503",
    "653",
    "2383",
    "6581",
    "22307"
  ],
  "discriminant": "3054801345415847256451965115791412312087805395457008085901580135193140055054688481722624",
  "regulator": "9151462517.56000249933263144585715028281624253584502087316649",
  "points": [
    [
      "1428145737661077/4",
      "982413753086123269065/8"
    ],
    [
      "-33396305934017358/121",
      "18104732597302590979327560/1331"
    ],
    [
      "444151511353302",
      "2739237248836895474520"
    ],
    [
      "-2789115401535375/16",
      "810420204084240657391281/64"
    ],
    [
      "902144847547302",
      "21728309615619535439280"
    ],
    [
      "1361874658708902",
      "45618933494107635138960"
    ],
    [
      "8952140649023846/25",
      "3025843060336703473944/125"
    ],
    [
      "20451359061529538",
      "2923339880171489386128360"
    ],
    [
      "-136426193682871991691/770884",
      "8592243858407511299576966032071/676836152"
    ],
    [
      "8762987347374879/25",
      "49632195787030978960908/125"
    ],
    [
      "2569954263485468694/6889",
      "133676638514328265158526416/571787"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/2xZ/2 X400a family y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=-44/2001. Family equations as posted by wgxli with curve #4252; section formulas from the Layr Labs Elliptic Rank Challenge repository (submission/research/x400a-family.gp, commit 7482bf9). T selected by our Mestre-Nagao sieve; PARI/GP 2.19 ellrank seeded with the family sections, bounds [11,11]; torsion Z/2xZ/2 (elltors).",
  "created_at": "2026-11-02 01:06:30",
  "updated_at": "2026-11-02 01:06:30"
}