{
  "id": 3045,
  "curve_key": "12266363699047487168842874934361:-42885824246240208123105753812603695741017874141",
  "ainvs": [
    "1",
    "0",
    "1",
    "-255549243730155982684226561133",
    "49636370655370589957824311621959424162853556"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 214.75324094272776,
  "faltings_height": 15.690356423454649,
  "conductor": "1373748530431186186949942270",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "41",
    "47",
    "61",
    "73",
    "101",
    "389",
    "1031",
    "53147"
  ],
  "discriminant": "3731644350991827475027681266057847730313914350140945824833224192443012863374180664062500",
  "regulator": "10033574.9216863613579236543673892437529705663596891295",
  "points": [
    [
      "1080750704793079/4",
      "-4484196680226685555303/8"
    ],
    [
      "959688212274610/9",
      "131163000626811758837134/27"
    ],
    [
      "-264314926319210",
      "-9935601524910475254458"
    ],
    [
      "20192307468522885",
      "-2868428937468835159972478"
    ],
    [
      "1716226683971050810/289",
      "-2240446377396472166097004029/4913"
    ],
    [
      "94111774828761157",
      "-28870858212331133841922632"
    ],
    [
      "1881844567162510/9",
      "62417489003083234739434/27"
    ],
    [
      "101738664853518864015/863041",
      "-3687196420813833687736167530512/801765089"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-065, rational kernel x=291804693239683. 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 20:34:43",
  "updated_at": "2026-09-26 20:34:43"
}