{
  "id": 2890,
  "curve_key": "645259187876987508142779841:-16390842157819455720284415879709112691361",
  "ainvs": [
    "1",
    "0",
    "0",
    "-13442899747437239752974580",
    "18970882127104731286461343053757984400"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 185.19508292881764,
  "faltings_height": 12.939130576798227,
  "conductor": "197790703710936583193310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "79",
    "197",
    "283",
    "347",
    "3203",
    "37853"
  ],
  "discriminant": "19834808732792188728990275118497597034101452366670295672224364343296000",
  "regulator": "1101464.461219221194436651404736734268545006488582142",
  "points": [
    [
      "2473914318080",
      "924811798245255500"
    ],
    [
      "2139183350950",
      "-56421828041053070"
    ],
    [
      "2261028565640",
      "-367486467194481460"
    ],
    [
      "3914994703590638/1849",
      "-59783678444937779656/79507"
    ],
    [
      "2135862463622696/961",
      "-8001969812854331580748/29791"
    ],
    [
      "177220049410771610/85849",
      "3314351283378990682621990/25153757"
    ],
    [
      "1371555317480",
      "1764460129371065420"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-124, rational kernel x=-1058632940440. 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 20:27:03",
  "updated_at": "2026-09-26 20:27:03"
}