{
  "id": 6427,
  "curve_key": "2773196383512176400:-4576963893396394727619288000",
  "ainvs": [
    "0",
    "0",
    "0",
    "-57774924656503675",
    "5297411913653234638448250"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 127.39959677368027,
  "faltings_height": 8.4768900653695,
  "conductor": "42313351568007232235600",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "19",
    "61",
    "101",
    "131",
    "173",
    "239",
    "1259",
    "1721"
  ],
  "discriminant": "219326415812428062112693530735486892303651600000000",
  "regulator": "1001929.16120505950258709701878429514486696860208770399",
  "points": [
    [
      "-32297515",
      "2670151291500"
    ],
    [
      "114779585",
      "422109966000"
    ],
    [
      "149628705",
      "51228206400"
    ],
    [
      "191702305",
      "1125540768000"
    ],
    [
      "202360835",
      "1375749759750"
    ],
    [
      "604375465/4",
      "1053782527875/8"
    ],
    [
      "8412129265/49",
      "227156583282000/343"
    ],
    [
      "10316878969/81",
      "51384900053872/729"
    ]
  ],
  "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=19/61.\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 [8,8]. The eight 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 42313351568007232235600.",
  "created_at": "2026-11-02 19:43:13",
  "updated_at": "2026-11-02 19:43:13"
}