{
  "id": 338,
  "curve_key": "41070310437028609048629219118801:-263909868945339879770129697163486714743514513049",
  "ainvs": [
    "1",
    "1",
    "1",
    "-855631467438096021846442064975",
    "305451237205254133961575716954767187528207317"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 218.38387364815233,
  "faltings_height": 16.00931179169078,
  "conductor": "7574847575418925340475858758748628717526303842283563568546909495282010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "571",
    "168062882960819311",
    "26568118382242454987",
    "191565698149509818162191"
  ],
  "discriminant": "-215413766000126800466521720643100270220386334713211058780295465294633003146387305267200000",
  "regulator": "4806019132545962067.726863555523846378628942727716867807241275704607592758426",
  "points": [
    [
      "9586890724415387",
      "-934461935779114035454094"
    ],
    [
      "8129199673154331",
      "-728394792241420409231246"
    ],
    [
      "28638444903465715/9",
      "-4661113179977735938988794/27"
    ],
    [
      "134171279221871019/49",
      "-46643764194443056548488258/343"
    ],
    [
      "3256072716032883114945/18861649",
      "1045478165108203724934815689773236/81916141607"
    ],
    [
      "196422946210587",
      "12040098259551536392306"
    ],
    [
      "618098292242515495/1156",
      "35547451921105752406539239/39304"
    ],
    [
      "1515067690314950403/2809",
      "138277234466923643715010442/148877"
    ],
    [
      "10261352988409163507/17161",
      "6205345600399569582765904646/2248091"
    ],
    [
      "8526007895786033103/13924",
      "5477212901272398822592722877/1643032"
    ],
    [
      "525938758437357743295963/314104729",
      "332487529501471124969436533792234822/5566878112067"
    ],
    [
      "60870243559983964753275/5230369",
      "14971790245713584704853356591836718/11961853903"
    ],
    [
      "10948352583275087",
      "1141611825337244763630806"
    ],
    [
      "53474554257282331",
      "12363920614128437121059954"
    ],
    [
      "973293186721147",
      "19866333665769180644786"
    ],
    [
      "4170049028301701579771133/12362548969",
      "10213884019127964331583983597024492078/1374554732216203"
    ],
    [
      "158181893980577376691427/3682561",
      "62897773204253778267905078224857694/7066834559"
    ],
    [
      "146263678576776715/9",
      "-55849027876027769835255794/27"
    ],
    [
      "-82454096071542520301/677329",
      "11257106036780956728997042947158/557441767"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,158,863,928,3783,3850], T=9037/2. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:18:51",
  "updated_at": "2026-08-24 19:18:51"
}