{
  "id": 6387,
  "curve_key": "3961613989921215386901895981888:-7792246728161896277078780260159802882782190080",
  "ainvs": [
    "0",
    "1",
    "0",
    "-82533624790025320560456166289",
    "9018804083520685772447732329707733184498031"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 211.36261291579436,
  "faltings_height": 15.485888190900432,
  "conductor": "2924624283892698709256938444686729792",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "23",
    "29",
    "31",
    "59",
    "79",
    "101",
    "103",
    "233",
    "379",
    "521",
    "617",
    "743",
    "2633"
  ],
  "discriminant": "842585481288295417795063337476835364488307312294424794528934669322913922802380661735424",
  "regulator": "724779992.578916028053009156240098770126821947468454045839999",
  "points": [
    [
      "186994939298482",
      "352286867736466870515"
    ],
    [
      "-29486346353897",
      "3380352405398394251760"
    ],
    [
      "222932412287581",
      "1303407404436171757932"
    ],
    [
      "436463363064505",
      "7492815757187041598856"
    ],
    [
      "-93655008666905",
      "-3990866940464966077824"
    ],
    [
      "431097441621021",
      "-7318201652421897674892"
    ],
    [
      "189248360339101",
      "-421153116674938507188"
    ],
    [
      "926292875459749/4",
      "-12197333258854084571769/8"
    ],
    [
      "147420976792495",
      "235602187058758290624"
    ],
    [
      "59330545168825",
      "2081078900071284159816"
    ],
    [
      "-144337434610775",
      "-4233730198739495204016"
    ]
  ],
  "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=521/466. 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 01:05:47",
  "updated_at": "2026-11-02 01:05:47"
}