{
  "id": 3034,
  "curve_key": "114332205582926778598124788416721:-998838378234276643367502584281866222206325891481",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2381920949644307887460933092015",
    "1156062937771153323922678483670947135438823225"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 221.44998325369312,
  "faltings_height": 16.458355866279632,
  "conductor": "11357092358577020158149155010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "37",
    "43",
    "47",
    "101",
    "149",
    "223",
    "283",
    "359",
    "379",
    "3561661"
  ],
  "discriminant": "287532236923454894119706249750797472867754200513402198488875730518568634681202936000000000000",
  "regulator": "5709888.93715248526944950572619785934728704207566214218",
  "points": [
    [
      "1272371267164730",
      "13610783611195456007585"
    ],
    [
      "143283255221570",
      "28595719341002078612885"
    ],
    [
      "10746842713203670/9",
      "102586397844975735784495/27"
    ],
    [
      "-731465657716954",
      "50069866125867420306557"
    ],
    [
      "683781524782652035670/11449",
      "-17874428724753204796938835129145/1225043"
    ],
    [
      "2250371866687430",
      "-84806420120493053778115"
    ],
    [
      "10508811325050280882070/17689",
      "-1077280821199456157467010362617655/2352637"
    ],
    [
      "5464689736590103670/4489",
      "-2338902792360839738927875345/300763"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-052, rational kernel x=-593182814314362. 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 20:34:14",
  "updated_at": "2026-09-26 20:34:14"
}