{
  "id": 2897,
  "curve_key": "833554171110046992545161:-5906424869012267608074054107050711909",
  "ainvs": [
    "1",
    "0",
    "1",
    "-17365711898125979011358",
    "6836139894688677403723829903428118"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 169.33820813411816,
  "faltings_height": 12.169184362151029,
  "conductor": "320501413516974788372430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "23",
    "29",
    "41",
    "101",
    "179",
    "359",
    "2129",
    "6733"
  ],
  "discriminant": "-19853409044529694970783772847942138446203746054697503257401212739790750",
  "regulator": "1222680.395753877724230612065044726678401279690837801",
  "points": [
    [
      "149314110078",
      "87017784915503143"
    ],
    [
      "177326219294",
      "96605779556465370"
    ],
    [
      "-177099713942/9",
      "-2286285771684195250/27"
    ],
    [
      "715564341702",
      "600667546117091770"
    ],
    [
      "37270185318222069/309136",
      "13851928092030198781478395/171879616"
    ],
    [
      "7425434711962369/46656",
      "-907196052548889286945685/10077696"
    ],
    [
      "994242042249814051689/3001286656",
      "-31813765713612864910681011186485/164422488162304"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-136, rational kernel x=110033611989. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by 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 20:27:22",
  "updated_at": "2026-09-26 20:27:22"
}