{
  "id": 3001,
  "curve_key": "3644275331679885271954865179120081:165025518343296003253694044074569204529852257589479",
  "ainvs": [
    "1",
    "0",
    "0",
    "-75922402743330943165726357898335",
    "-191001757341777787870494261104626287571932900775"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 231.8353968086641,
  "faltings_height": 17.339218633293456,
  "conductor": "35144361650725361785516703913690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "23",
    "37",
    "41",
    "43",
    "47",
    "139",
    "181",
    "797",
    "11813",
    "1518463"
  ],
  "discriminant": "12248415091634378937162944077391173844353929821283451628334995048984987729745327078481330176000000",
  "regulator": "6882814.63256508112751295670282577474931471315137581466",
  "points": [
    [
      "10309376425153766",
      "-349284367786641534886003"
    ],
    [
      "-242479138437557650/49",
      "86449092291088231524860795/343"
    ],
    [
      "-5984382020317730",
      "221425520055532005206365"
    ],
    [
      "-4790707216745050",
      "250538063077903474495565"
    ],
    [
      "-358337474696303530/121",
      "118054560800669350424393815/1331"
    ],
    [
      "2887429204915648797046105/7354944",
      "-4905229549640693087927814674988614855/19946608128"
    ],
    [
      "75773783216838926379157356230/2675164461649",
      "-19754498810680871631472151695536624133763195/4375480267321872857"
    ],
    [
      "2862439829748093241670/271441",
      "-60175960205894603889505717546235/141420761"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-115, rational kernel x=22456707641669839/4. 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 20:32:47",
  "updated_at": "2026-09-26 20:32:47"
}