{
  "id": 6398,
  "curve_key": "20617992622210117073367730624:-2157875306705552820555636691414425232325632",
  "ainvs": [
    "0",
    "1",
    "0",
    "-429541512962710772361827721",
    "2497540864242394806249888229990723409655"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 195.58788490104268,
  "faltings_height": 14.322549235366608,
  "conductor": "58255187586444887551054174315287359040",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "31",
    "61",
    "107",
    "109",
    "131",
    "191",
    "419",
    "439",
    "823",
    "977",
    "2281",
    "7057"
  ],
  "discriminant": "2377497812967454207170728533165398296865227704660092419002363149181356572991590400",
  "regulator": "1394043449.59525687426335219684430921566091664953649984383192",
  "points": [
    [
      "575116627151607",
      "13783342812814275802200"
    ],
    [
      "5468058539187",
      "-17671328202295825200"
    ],
    [
      "-2473075722198",
      "59537416508258164515"
    ],
    [
      "6185207051319",
      "8795670162923335224"
    ],
    [
      "-11603673713709",
      "76937773250129223264"
    ],
    [
      "21887711530617",
      "-59846871588730673460"
    ],
    [
      "2904563984833695/49",
      "147657042726988588796640/343"
    ],
    [
      "-15847431444813",
      "-72970743736745838000"
    ],
    [
      "5114615798889537/256",
      "-178095136316367588618465/4096"
    ],
    [
      "76857076697390370/12769",
      "16462771919588462883813255/1442897"
    ],
    [
      "-23124207348273",
      "8072447067621303840"
    ]
  ],
  "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=1045/17. 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 01:20:09",
  "updated_at": "2026-11-02 01:20:09"
}