{
  "id": 6429,
  "curve_key": "5527945396395328:-404539576356450180538880",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-115165529091569",
    "468217140652919628369"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 108.74577781105597,
  "faltings_height": 6.9473548702136485,
  "conductor": "24182946965166528",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "67",
    "179",
    "443",
    "499",
    "617"
  ],
  "discriminant": "3050742652492683895029327448697770980163584",
  "regulator": "13952.70482201005581377880683850238447625891152895888",
  "points": [
    [
      "-1684224",
      "25639894665"
    ],
    [
      "5494213",
      "1150454480"
    ],
    [
      "17251651",
      "60131925140"
    ],
    [
      "-594805095/64",
      "13888218981021/512"
    ],
    [
      "446281747/81",
      "709642840060/729"
    ],
    [
      "835655416/289",
      "62026009870517/4913"
    ],
    [
      "116910813205/9409",
      "28213438126027616/912673"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/2xZ/2 X400a family y^2=x(x+A)(x+B), with\r\nA=q(121q-99p)(26p-23q)(75p-44q),\r\nB=p(21q-74p)(25p-36q)(p+77q),\r\nat T=p/q=7/22.\r\n\r\nFamily equations as posted by wgxli with curve #4252:\r\nhttps://elliptic-rank.icarm.cloud/curve/4252\r\n\r\nSection formulas from the Layr-Labs elliptic-rank-challenge-public repository, submission/research/x400a-family.gp, commit 7482bf9:\r\nhttps://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/7482bf9/submission/research/x400a-family.gp\r\n\r\nThis specialization was identified in a small-height rational-parameter enumeration with a Mestre–Nagao prescreen. A separate replay using the family sections returned rank bounds [7,7]. The seven displayed points were checked exactly on the global minimal model, and the torsion subgroup was computed as Z/2xZ/2.\r\n\r\nThe minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. The conductor is 24182946965166528.",
  "created_at": "2026-11-02 19:48:11",
  "updated_at": "2026-11-02 19:48:11"
}