{
  "id": 6428,
  "curve_key": "2413790329784016516025:-116468099918679788172828238286125",
  "ainvs": [
    "1",
    "0",
    "1",
    "-50287298537167010751",
    "134801041568355442914528024898"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 147.70645564754312,
  "faltings_height": 10.199917956105631,
  "conductor": "78826852240827807202350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "71",
    "103",
    "229",
    "421",
    "449",
    "521",
    "1549"
  ],
  "discriminant": "288686614328288874770261368358919792971595524885692256250000",
  "regulator": "9871605.3925462453439802373107037002653122085013425628928",
  "points": [
    [
      "1804434587",
      "223462990321956"
    ],
    [
      "14420703623/4",
      "152618620307373/8"
    ],
    [
      "4560753812",
      "17855497884906"
    ],
    [
      "20326567403/4",
      "819058751432343/8"
    ],
    [
      "5098065587",
      "104559444241956"
    ],
    [
      "52185449117/16",
      "4738133131527609/64"
    ],
    [
      "84815856551/25",
      "7119016772513184/125"
    ],
    [
      "17912475202547/8281",
      "143269693979108910576/753571"
    ],
    [
      "18246930194303/5041",
      "5088653798354681544/357911"
    ]
  ],
  "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=64/5.\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 [9,9]. The nine 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 78826852240827807202350.",
  "created_at": "2026-11-02 19:46:19",
  "updated_at": "2026-11-02 19:46:19"
}