{
  "id": 3186,
  "curve_key": "1145756358777515323932807721:-63143482584894898792456560745645787492992981",
  "ainvs": [
    "1",
    "0",
    "1",
    "-23869924141198235915266828",
    "73082734473257982724331044652051853696506"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 201.70796708782777,
  "faltings_height": 14.866654118566517,
  "conductor": "160217014633589313145585973576996191511802644586870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "31",
    "43",
    "109",
    "113",
    "223",
    "233",
    "281",
    "467",
    "3109",
    "5441",
    "102031",
    "1148507",
    "29485399"
  ],
  "discriminant": "-2307348315305855930627187360038199656477517988388171855018247560817219758044844550000",
  "regulator": "1564774134187081.11984933526168249032116397704098685075970553360262",
  "points": [
    [
      "9940242686605",
      "-271712428968492642253"
    ],
    [
      "-26965344324935",
      "-232635086872892992813"
    ],
    [
      "11605656304330",
      "272706592555483007747"
    ],
    [
      "44661778467730",
      "401375574677567219522"
    ],
    [
      "683782069570",
      "-270308587617340913893"
    ],
    [
      "-41848547446470",
      "28147069457527213747"
    ],
    [
      "2374225514355970/49",
      "147801962771457380557646/343"
    ],
    [
      "1841085442195645/49",
      "-121380112054247265117079/343"
    ],
    [
      "9149470611795778/169",
      "-1054725936903635784048409/2197"
    ],
    [
      "31868761274617056745/304704",
      "-185373621648198605571111350449/168196608"
    ],
    [
      "1214258078975038152447057333505/86466713379868441",
      "-6987078182803909502642779691949024026684516417/25425729803654438802804989"
    ],
    [
      "168883209147820824047318005/789176382736",
      "-2202321199230670788231179385915129303923/701069574661822016"
    ],
    [
      "2419843639400480409510441143350365/5487431991435331921",
      "-119080134318259752346036828529840615827138569938407/12854456717124483157815927719"
    ],
    [
      "-1410238896503604387126613809808807655/35788553153105271182689",
      "-767129465301277749679284916572818177942042305791460861/6770429370475130134719407846645137"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-060, rational kernel x=335995856219831/4. Source: https://dujella.github.io/tors/z2old141516171819.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 20:41:39",
  "updated_at": "2026-09-26 20:41:39"
}