{
  "id": 6419,
  "curve_key": "1983743435216096064:-2787868897973248743798962688",
  "ainvs": [
    "0",
    "0",
    "0",
    "-41327988233668668",
    "3226700113394963823841392"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 126.39455207239793,
  "faltings_height": 8.335923157830212,
  "conductor": "43672605438900505763520",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "23",
    "31",
    "43",
    "59",
    "79",
    "97",
    "109",
    "191",
    "281"
  ],
  "discriminant": "19843512430410860719757612541000683087845671321600",
  "regulator": "108281.780317719679335131711660905700630751686806460478",
  "points": [
    [
      "72754546",
      "777822086800"
    ],
    [
      "915234426",
      "27056454503760"
    ],
    [
      "-81844899",
      "2461897625715"
    ],
    [
      "108557634",
      "139846861728"
    ],
    [
      "243511794",
      "2757282794928"
    ],
    [
      "-592870551/4",
      "-19752261561045/8"
    ],
    [
      "123273861",
      "73238385825"
    ],
    [
      "128358826",
      "-191641767040"
    ]
  ],
  "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=55/46. 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 [8,8]; torsion Z/2xZ/2 (elltors).\r\n",
  "created_at": "2026-11-02 14:16:04",
  "updated_at": "2026-11-02 14:16:04"
}