{
  "id": 3066,
  "curve_key": "8984777872994338087990278081:-681936231456082093899581522102058281613729",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-187182872354048710166464127",
    "789278045666808478472233792388257219751"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 193.09598792636237,
  "faltings_height": 14.09978197842488,
  "conductor": "110072036541366600851273211270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "37",
    "41",
    "59",
    "67",
    "257",
    "3203",
    "48539",
    "173659"
  ],
  "discriminant": "150619358850115477130021527951035002334995235897056476256679076854947226683040000",
  "regulator": "83182465.102554224727810228893765146290598724799199290308",
  "points": [
    [
      "447638361211219/9",
      "-9137078726996872948622/27"
    ],
    [
      "3720797550501",
      "12013342315304651074"
    ],
    [
      "12526540512981",
      "-20251339821794173886"
    ],
    [
      "48808621503591",
      "-328525545087433361006"
    ],
    [
      "385014297035422851/7921",
      "-230094619899247531126008874/704969"
    ],
    [
      "-33549787569",
      "28205636926931620714"
    ],
    [
      "16494172313806395402081/384905161",
      "-2018654839811212368008972399987194/7551454353659"
    ],
    [
      "364543020725225611/34225",
      "-12566897855809576170206914/6331625"
    ],
    [
      "694734213184393646151/62710561",
      "-4308125942303475270151884519154/496604932559"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-042, rational kernel x=7718659159251. 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 20:35:39",
  "updated_at": "2026-09-26 20:35:39"
}