{
  "id": 6421,
  "curve_key": "2572957047270092224:1230000620329777885535853568",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-53603271818126921",
    "-1423611811217633798513079"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 127.17476254024605,
  "faltings_height": 8.660507289289976,
  "conductor": "7290134835250249699654080",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "47",
    "103",
    "179",
    "263",
    "401",
    "409",
    "883",
    "1609"
  ],
  "discriminant": "8981685139825832320914599277720264174856510649241600",
  "regulator": "1243485.34741533757334716008330936625413688944621291723",
  "points": [
    [
      "-204092959",
      "1007553209520"
    ],
    [
      "-11230321169/81",
      "1332917308765900/729"
    ],
    [
      "-195527272",
      "1257816886599"
    ],
    [
      "-102669232",
      "1731346733301"
    ],
    [
      "1665745661",
      "67314528824400"
    ],
    [
      "22313810261/49",
      "2840928806634360/343"
    ],
    [
      "-38907633631/784",
      "23173019356076535/21952"
    ],
    [
      "-174604619/4",
      "-7301765144635/8"
    ]
  ],
  "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=-110/13. 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 14:17:06",
  "updated_at": "2026-11-02 14:17:06"
}