{
  "id": 6416,
  "curve_key": "1851697679920285968:-2285433230964100936684908480",
  "ainvs": [
    "0",
    "0",
    "0",
    "-38577034998339291",
    "2645177350652894602644570"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 126.18790367102365,
  "faltings_height": 8.485839478342724,
  "conductor": "4254224472462433385668752",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "29",
    "41",
    "107",
    "113",
    "293",
    "463",
    "571",
    "1559"
  ],
  "discriminant": "651543331035537706902389363677642298194257692550144",
  "regulator": "474170.092577881494199105659640816537254090228011078602",
  "points": [
    [
      "10304003907",
      "1045756647681174"
    ],
    [
      "141788217",
      "160948008144"
    ],
    [
      "762446853",
      "20407395975732"
    ],
    [
      "-4282970739/25",
      "256962970609884/125"
    ],
    [
      "-133898139",
      "2325929797620"
    ],
    [
      "3511482955/9",
      "185079032420590/27"
    ],
    [
      "648427819",
      "-15819855602950"
    ],
    [
      "209740660197/961",
      "-64046610753044724/29791"
    ]
  ],
  "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).\r\n",
  "created_at": "2026-11-02 14:14:29",
  "updated_at": "2026-11-02 14:14:29"
}