{
  "id": 3111,
  "curve_key": "478945408974810651174325774976703787853668063213521:-10481314569184533823291211977036243919208297520546356320674417261779472492569",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-9978029353641888566131786978681328913618084650282",
    "12131151121741358591772238579040028131778041440986508930372063198247403881"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 350.0870132576785,
  "faltings_height": 26.833750318163027,
  "conductor": "7882602549544199351275160289497567761080531375360072630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "29",
    "47",
    "73",
    "113",
    "173",
    "229",
    "251",
    "751",
    "1861",
    "2351",
    "3919",
    "4007",
    "4639",
    "42569",
    "134999",
    "321569"
  ],
  "discriminant": "3884216391571627352247148103129080677244623863456029601226759538509684066075959228151047326082283331910026298513999904959389078955441899776000000",
  "regulator": "12263635546002.1125555699708271264978039992516041862658627643",
  "points": [
    [
      "1865677824830166637375041",
      "-96582083595766139279175511279820921"
    ],
    [
      "2049943383615605961773841",
      "-539599013498770943624190438434633321"
    ],
    [
      "5780219385295850823039409",
      "-12148188885367916322897700529267837609"
    ],
    [
      "41039496537777927201075963801/22201",
      "-181538486428174726794864822311201659852309/3307949"
    ],
    [
      "614281959890020138027070943459229369/70244611369",
      "453602676744624232478413437369051327921784236011309027/18617421063405653"
    ],
    [
      "187819734658600373493084091449/6889",
      "80873990474283726857907332214155439720267773/571787"
    ],
    [
      "175623214535052408563592261570258374748131181/316399363912466641",
      "-2327372325650317584609007444815665903577625075173475775462261493019/177972705520255977354190439"
    ],
    [
      "463845130361627272273852795928401476441/238396163046889",
      "-1059274998151893139387017635412553090518933141036217701827/3680856544325499051787"
    ],
    [
      "1598807711200230798134551871941999/871253289",
      "-469553401199557324071326807567127566006429568973/25716783331413"
    ],
    [
      "1368131356348895679142638266309487209080724064512520169/719893662234973204214305661881",
      "-109760026226888607626770703588500806121431710557359633077715428617754896576017301/610804918064109626749873495544774467997586221"
    ],
    [
      "1491619748735181883113906157570254579009/728197726849321",
      "-10528187964646629859966068914846597656263051096891458102291/19650516878512959240619"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-018, rational kernel x=-907749466601149462784559. 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 20:37:48",
  "updated_at": "2026-09-26 20:37:48"
}