{
  "id": 3016,
  "curve_key": "-14169313671492459327912690688031:-461837475886868789464402818792374683120357073233",
  "ainvs": [
    "1",
    "0",
    "0",
    "295194034822759569331514389334",
    "534534115609801864257376534758175549756242020"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 219.5030844602574,
  "faltings_height": 16.35159638213388,
  "conductor": "2958865796524431023234757779070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "23",
    "29",
    "37",
    "41",
    "43",
    "53",
    "59",
    "71",
    "73",
    "12569",
    "3131981"
  ],
  "discriminant": "-125080219586307745595131541638458069559166852117722698172166098995431101366098847179464103360",
  "regulator": "752657465.959773324801349246137556600239257430899817981",
  "points": [
    [
      "10636318943609816",
      "1098623995752019639133810"
    ],
    [
      "27558445579082966",
      "4575852370271083746147674"
    ],
    [
      "36511571628856480/9",
      "7066546611864758671832050/27"
    ],
    [
      "13454002593511539896/134689",
      "-1174976455453705143143914304470/49430863"
    ],
    [
      "12479792326037108720/22801",
      "100971410823712337126889820730/3442951"
    ],
    [
      "-4127709764196076826/10201",
      "-19243072248512152617417521614/1030301"
    ],
    [
      "5217928767668516",
      "-379660689846054020286226"
    ],
    [
      "8399929116702949664",
      "-24345204830416552880818193674"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-030, rational kernel x=345678105543668. 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 20:33:25",
  "updated_at": "2026-09-26 20:33:25"
}