{
  "id": 6415,
  "curve_key": "1580843922427167168:566915169777872459155522560",
  "ainvs": [
    "0",
    "0",
    "0",
    "-32934248383899316",
    "-656151816872537568467040"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 125.71347151936352,
  "faltings_height": 8.539225501811218,
  "conductor": "1238609546663682784153024",
  "bad_primes": [
    "2",
    "7",
    "11",
    "17",
    "19",
    "29",
    "37",
    "47",
    "71",
    "79",
    "109",
    "769",
    "887"
  ],
  "discriminant": "2100256290839300465334827427291669581795735183724544",
  "regulator": "1043329.52441410496990458165171866330314317390801195317",
  "points": [
    [
      "-38066747",
      "736468755483"
    ],
    [
      "648970717",
      "15852221736351"
    ],
    [
      "-1039636508/9",
      "34225601204564/27"
    ],
    [
      "211154613",
      "-1343214957843"
    ],
    [
      "-20309448",
      "-65935387944"
    ],
    [
      "-68022428",
      "1126664323884"
    ],
    [
      "1505098682",
      "57959535668496"
    ],
    [
      "-3091022886108/18769",
      "-1410848431336194444/2571353"
    ]
  ],
  "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=-374/37. 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).",
  "created_at": "2026-11-02 14:10:53",
  "updated_at": "2026-11-02 14:10:53"
}