{
  "id": 3121,
  "curve_key": "90913666021543747097275125378789103720321:21569774431909149988490495396745954645367387836608050816509119",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1894034708782161397859898445391439660840",
    "-24965016703598553227577391083076701696774653385041938046400"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 282.9321868737666,
  "faltings_height": 21.589467757911873,
  "conductor": "31000471439531693917957022221199714058221545530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "41",
    "67",
    "71",
    "73",
    "103",
    "127",
    "293",
    "1091",
    "682327",
    "102838432973"
  ],
  "discriminant": "165609415571190820129341365232069571270124372402764583095561961310796627580712177957014655281457550022615611022828160000",
  "regulator": "1689537981991.91455143431322266739176514950284828901413625782",
  "points": [
    [
      "270520363505805001260",
      "-4388585534829895271467133883540"
    ],
    [
      "216829221525603796410",
      "-3123869320474969790700763756620"
    ],
    [
      "49955574794449754640",
      "-71305663538328353947751925000"
    ],
    [
      "1022983896738424713360",
      "-32689234897974033976782513476040"
    ],
    [
      "5922447628031699030160",
      "-455764076888700953850257694834120"
    ],
    [
      "47695513110379260585420/529",
      "8917679408948952181437551485480920/12167"
    ],
    [
      "69788135118789775560",
      "-427491328683066413936041976040"
    ],
    [
      "1044022590661252763618352867390/2796188641",
      "-1059226367827156612544574501353960335960279710/147859659147439"
    ],
    [
      "3138816300197070173811648/6889",
      "-5534784702807214459827258354138681336/571787"
    ],
    [
      "2200922517635020411958922467578560/10790916212209",
      "-100720506600816079858020777783316362601522074032280/35447652584044591177"
    ],
    [
      "193800494264237537790820/9",
      "85316186113891562684060478449757020/27"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-004, rational kernel x=17040500771125811280. 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 20:38:16",
  "updated_at": "2026-09-26 20:38:16"
}