{
  "id": 6395,
  "curve_key": "554328235448458640158353468049:-410030775552684762101382568520593204149336793",
  "ainvs": [
    "1",
    "0",
    "0",
    "-11548504905176221669965697251",
    "474572656889680475241932171102584452105480"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 205.46266351469058,
  "faltings_height": 14.968681093446662,
  "conductor": "11419688444618190533967482030520035564715",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "19",
    "31",
    "37",
    "89",
    "137",
    "167",
    "191",
    "283",
    "509",
    "929",
    "1213",
    "1511",
    "6779",
    "63781"
  ],
  "discriminant": "1278141394171205177984272845611043493839640919570054423612950613854522268188659036225",
  "regulator": "10478764436.5466909102900764881760955892356752534114868184003",
  "points": [
    [
      "-23791445259622008/529",
      "11561787906554571864789012/12167"
    ],
    [
      "4587714695548632/529",
      "7451444008591138463923032/12167"
    ],
    [
      "36539573202483",
      "318403306568314280946"
    ],
    [
      "150493378831475583/1681",
      "27415038761820619198359711/68921"
    ],
    [
      "57128975208722757/529",
      "8490020779187285606633382/12167"
    ],
    [
      "-19769820963916533/169",
      "1041410283488492114797527/2197"
    ],
    [
      "79818538540839",
      "-247612054598344204785"
    ],
    [
      "85488718404815659887/332929",
      "729973615970573793556083179418/192100033"
    ],
    [
      "41820359437727606187/850084",
      "125161003106405609123975828043/783777448"
    ],
    [
      "1693023039752180074612/21372129",
      "23556549440918224664139595854742/98803352367"
    ],
    [
      "57792914166855",
      "13433025514429141770"
    ]
  ],
  "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=2960/573. 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 01:16:30",
  "updated_at": "2026-11-02 01:16:30"
}