{
  "id": 343,
  "curve_key": "2077722313129462812428790919879281:-94707351072105997800532588693075585241496086061321",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-43285881523530475258933144164152",
    "109614989666789360127642358536641482836869473979"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 230.14975217146204,
  "faltings_height": 16.791857773555815,
  "conductor": "50942599871541069354056504921648280000071055124980383441294377459196586533970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "8768717",
    "151942966871",
    "459535661555689",
    "645058738193217419",
    "6857363496744081905501"
  ],
  "discriminant": "-58182934520641038384251737838573035416513937358706673216587586437986300447298128185328640000",
  "regulator": "142470474246966436202.2068711643981879579231795504385081941117192671659308500",
  "points": [
    [
      "10300201881431681541/25",
      "-33053204234615102579744642779/125"
    ],
    [
      "67440588834602259",
      "-17433470796488479171879727"
    ],
    [
      "26305577587794169",
      "-4144149891548775086682543"
    ],
    [
      "1253025071323627581/1849",
      "22571077665952629155694830611/79507"
    ],
    [
      "2898164418726281709/2401",
      "28607049444422613519402045433/117649"
    ],
    [
      "2162911440499081835413/683929",
      "37317821686993197983715011926923/565609283"
    ],
    [
      "805006435096777789088877/214300321",
      "14273685517551851498901877985847239/3137142399119"
    ],
    [
      "218524850133302208941613/57866449",
      "1095031012143441974860533435329183/440190077543"
    ],
    [
      "103436647643503776191773/27279729",
      "152189280606669150321755032574927/142482024567"
    ],
    [
      "3797385773917737",
      "792825778477831830181"
    ],
    [
      "4671288627586987",
      "96674919376191279478081"
    ],
    [
      "1638640481144528877194997/344436481",
      "681370476719222173250554948242143599/6392396650879"
    ],
    [
      "88367861778264817",
      "26198062363001806352982081"
    ],
    [
      "32713710531533653/9",
      "468748128376139293239187/27"
    ],
    [
      "1098786131269157487711389437/20335045201",
      "36164246426922687171551889485693092857281/2899797780707801"
    ],
    [
      "5494276783500143547247/1418481",
      "13607441002995250935553485117151/1689410871"
    ],
    [
      "817560845382286558572957/216119401",
      "5841488894703062831449953932135461/3177171314101"
    ],
    [
      "49601422640478456723933/29997529",
      "33895265503831280222476187784628373/164296466333"
    ],
    [
      "17248096730967104320958900253/6647182273369",
      "2082624846828637460677989855139852181529757/17137851750569509597"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=14639/10. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:19:13",
  "updated_at": "2026-08-24 19:19:13"
}