{
  "id": 3086,
  "curve_key": "112772883609005556861633458820374593:-37775185226496598933724166127464573282359439307980385",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2349435075187615767950697058757804",
    "43721279197334026347875973048560460636469040598864"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 242.13205195629337,
  "faltings_height": 17.986185229296762,
  "conductor": "86459235830591416435905931905748037526",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "41",
    "43",
    "73",
    "1367",
    "1931",
    "5905499",
    "29036999"
  ],
  "discriminant": "4195432898049177133335195048046525048583929454311274641232013549607663097627936773262100490817799744",
  "regulator": "27634049171.65227236786783995102147588761015388047312706237",
  "points": [
    [
      "30015344123370478",
      "-493586123569157845227344"
    ],
    [
      "53236660073998228",
      "8338192565460008471136916"
    ],
    [
      "31228429798505578",
      "-898074995982478155112874"
    ],
    [
      "60707015819686636",
      "11172295527706439370767092"
    ],
    [
      "34992341074424386",
      "2087080556277450811602622"
    ],
    [
      "1070068163212348942",
      "1105805950210327823586399664"
    ],
    [
      "109451982769055977978/2809",
      "-501218882642242095414014483392/148877"
    ],
    [
      "32211407654827228",
      "-1210129159170633110988944"
    ],
    [
      "81272949236295721470681028/2052180601",
      "-332479389825430560125276657596391239484/92965833405901"
    ],
    [
      "351646291300680028",
      "206640783436843805124714736"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-029, rational kernel x=-13413637921750568. 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 20:36:37",
  "updated_at": "2026-09-26 20:36:37"
}