{
  "id": 3084,
  "curve_key": "1033702771060620688275167342625177361:-1050941458286587930374689927454014314714241736081563641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-21535474397096264339065986304691195",
    "1216367428572439732435342327387827873034132780259025"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 248.7786318812841,
  "faltings_height": 18.39496872696777,
  "conductor": "20468006001635161782527819002994903297490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "41",
    "43",
    "59",
    "151",
    "173",
    "271",
    "4273",
    "697441",
    "1256873"
  ],
  "discriminant": "44141760873677415861571794333222999999249119945589980584303467843847382090800962970497125039062440000",
  "regulator": "6096263023.946316026307705651387466008600365798475758355355",
  "points": [
    [
      "98693634389304010",
      "7229935746013386672926905"
    ],
    [
      "87661719875151400",
      "-1474432969930603755102305"
    ],
    [
      "86718259817155120",
      "-987312232663747713637145"
    ],
    [
      "90950437786522930",
      "-3169700445461425815605435"
    ],
    [
      "86003734012146370",
      "-612430086349329528055895"
    ],
    [
      "19375956111356666347460562460/70527956041",
      "-2371795182192450062322259941196788672145615/18730179813764411"
    ],
    [
      "793645949064526360/9",
      "-47051199638300693554094365/27"
    ],
    [
      "342556563872039923/4",
      "-3305367983268564516426529/8"
    ],
    [
      "140483205699807231902740/1646089",
      "-496193825395397786712406444867015/2111932187"
    ],
    [
      "6871825747499521202904576161175859735/80526425155964351524",
      "-166201269419155881394315588772288222942964809805106865/722616093445217921000098518232"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-024, rational kernel x=-42159575397842210. Source: https://dujella.github.io/tors/z4old9101112.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 20:36:29",
  "updated_at": "2026-09-26 20:36:29"
}