{
  "id": 6422,
  "curve_key": "369217029073104427654800:-221135169385263167422451449987320000",
  "ainvs": [
    "0",
    "0",
    "0",
    "-7692021439023008909475",
    "255943483084795332664874363411250"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 162.79701473606994,
  "faltings_height": 11.447426114973675,
  "conductor": "4333929710712664354099132525200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "37",
    "43",
    "47",
    "53",
    "83",
    "97",
    "139",
    "241",
    "311",
    "487"
  ],
  "discriminant": "828327951119249971414856393170815284012659902832626512805264000000",
  "regulator": "6186672.587876234440147012314298070952559793770636191364516",
  "points": [
    [
      "38483358129",
      "4113553458311892"
    ],
    [
      "41676642685",
      "2784921521006800"
    ],
    [
      "45563170785",
      "244651776093900"
    ],
    [
      "57489279075",
      "1933331988223350"
    ],
    [
      "33962802075",
      "5820310994711850"
    ],
    [
      "-17504101035",
      "19627079757516000"
    ],
    [
      "11051705685",
      "13125676498552800"
    ],
    [
      "225742032225/4",
      "10073495328723225/8"
    ],
    [
      "-1175935529175/16",
      "-1318269492175711275/64"
    ],
    [
      "511332664165/9",
      "41093425513363600/27"
    ]
  ],
  "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=2651/1577. 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 [10,10]; torsion Z/2xZ/2 (elltors).",
  "created_at": "2026-11-02 16:05:07",
  "updated_at": "2026-11-02 16:05:07"
}