{
  "id": 2751,
  "curve_key": "1368245994686636204176:15908136724645285873798522016576",
  "ainvs": [
    "0",
    "1",
    "0",
    "-28505124889304920920",
    "-18412195292655974354072151900"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 146.00344972976066,
  "faltings_height": 10.228900818278111,
  "conductor": "572097030360240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "107",
    "167",
    "91183"
  ],
  "discriminant": "1335891520482143451624482869033194995963828610727539600000000",
  "regulator": "5887.354166120761594549236770557365673020506177",
  "points": [
    [
      "-4522446735165/961",
      "3196472277433393800/29791"
    ],
    [
      "8466656422225/576",
      "-22876529894327847815/13824"
    ],
    [
      "2734961426291565/252004",
      "-123336652042860053359275/126506008"
    ],
    [
      "9628078329489414600/185761",
      "-29875103596638960163837315290/80062991"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#824 via the rational 2-torsion point x=9961626491. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:20:40",
  "updated_at": "2026-09-26 20:20:40"
}