{
  "id": 3128,
  "curve_key": "116885278495142989644015720084832240757098018225:-39961145655810795479061022226760960366106557831301648881167020102399625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-2435109968648812284250327501767338349106208713",
    "46251325990521754026689983318486396751949337631251172036297849383406"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 325.1325663384525,
  "faltings_height": 24.699055428125664,
  "conductor": "326885688138289438101160708711925723710232867288025",
  "bad_primes": [
    "3",
    "5",
    "7",
    "19",
    "31",
    "37",
    "41",
    "53",
    "73",
    "83",
    "97",
    "109",
    "157",
    "271",
    "359",
    "431",
    "449",
    "457",
    "797",
    "1447",
    "3061",
    "6148501"
  ],
  "discriminant": "7631854496070135847948811569256638078651460559877101792277786672630094212981289373425852593952779386796340056096436718303939252890625",
  "regulator": "3402742020973.65707153107829281733749692907823427641493266648",
  "points": [
    [
      "2904461205393356616749568370/101761",
      "-196259304746224466173105459227884035557/32461759"
    ],
    [
      "2336758164503567963573146/81",
      "75891312257818910050131295384379600/729"
    ],
    [
      "44620034734216376701146",
      "5141282057754470438558285970038005"
    ],
    [
      "264949352425176615239434/9",
      "-7518507629236795409756498212876880/27"
    ],
    [
      "2333005701994781703380313654162084/80787261361",
      "-2591089264917084454628104716727912103034692543278/22962244083898391"
    ],
    [
      "669051322617160123393807354/23409",
      "-80911793908565648777652413965551928720/3581577"
    ],
    [
      "28249476777825481619230",
      "68966919135415511094965346852397"
    ],
    [
      "252796269802836187596490557241/8162449",
      "-17150151525785729185288845369671070910309941/23320116793"
    ],
    [
      "246717565079580214509107770/6561",
      "1489473360080585162901430465465866830032/531441"
    ],
    [
      "1185630665602514780864786278200639871/9993450982564",
      "-1193519699594630110616373468129293666780154113208316989/31591716971022584488"
    ],
    [
      "17559874871246370713569321/625",
      "1785408258544403483197621618853651919/15625"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z2old1011121314-056, rational kernel x=-228301316031920956063565/4. Source: https://dujella.github.io/tors/z2z2old1011121314.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 20:38:35",
  "updated_at": "2026-09-26 20:38:35"
}