{
  "id": 3087,
  "curve_key": "6310081344867026072238867400336:-7409032640877080887403291142911635176855390016",
  "ainvs": [
    "0",
    "1",
    "0",
    "-131460028018063043171643070840",
    "8575269260274355355225951320318520536633088"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 212.75910407313745,
  "faltings_height": 15.783332994561016,
  "conductor": "145656839839920898983128703362734440",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "31",
    "43",
    "47",
    "53",
    "149",
    "461",
    "7129",
    "100384235521"
  ],
  "discriminant": "113631679952406301225296106120680091906448905169455844952725273966266776236538288131097600",
  "regulator": "98251214458.51571513529163459311540205513868911831414668388",
  "points": [
    [
      "-14340159331129",
      "3233802420515284516080"
    ],
    [
      "34449745668128",
      "2021729252430622645152"
    ],
    [
      "-33000559371829",
      "3588535201500468410670"
    ],
    [
      "-409662858993467584/3721",
      "-1057689894175075114716606480/226981"
    ],
    [
      "67478722455968",
      "108492602645051456832"
    ],
    [
      "33826207112344184/529",
      "-7984776310091641866165360/12167"
    ],
    [
      "16527924784243888049794261/837870916",
      "-67182221565453097205819286713168793495/24253011534536"
    ],
    [
      "-176874142617582664/841",
      "126542366209581341192475120/24389"
    ],
    [
      "34582091026953368/961",
      "58766179066002806311916352/29791"
    ],
    [
      "6264526202834822291/19321",
      "-519646724481086706322242270/2685619"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-023, rational kernel x=195804468832796. 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 20:36:40",
  "updated_at": "2026-09-26 20:36:40"
}