{
  "id": 4172,
  "curve_key": "120340358806766211729:-3523771079480556388309894008633",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-2507090808474296078",
    "4078438750025564818217988381"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "naive_height": 140.67416907073093,
  "faltings_height": 9.774943751922205,
  "conductor": "30066338547903581129348879285312931560456912310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "47",
    "499",
    "6709",
    "80248601",
    "467823647",
    "3179504860341203"
  ],
  "discriminant": "-6177209130104430645594498722574206322842373406341019238400",
  "regulator": "154622977862451.8101235780512184581624797136829236358509839124554133113",
  "points": [
    [
      "1663310025",
      "67156322735027"
    ],
    [
      "1230965598921",
      "-1365742144156772989"
    ],
    [
      "281390890659609/172225",
      "4710557310624278314893/71473375"
    ],
    [
      "86615885504745/8281",
      "-798279623229000297783/753571"
    ],
    [
      "-1035163129351/9409",
      "60215260052280484563/912673"
    ],
    [
      "296873776691105/160801",
      "4886355868345728507987/64481201"
    ],
    [
      "-223238782875895/165649",
      "-4771752286378817056539/67419143"
    ],
    [
      "9428328112625/5929",
      "29277916161396534591/456533"
    ],
    [
      "-974396079136295/690561",
      "-39785179924648266108883/573856191"
    ],
    [
      "4588794004859/6724",
      "28571728716609191853/551368"
    ],
    [
      "497203104619431629/444577225",
      "484671279127058106342951147/9373910789125"
    ],
    [
      "9803515920875/2809",
      "28959483192488153229/148877"
    ],
    [
      "3883327577",
      "230006903413011"
    ],
    [
      "1649003448811321/1640961",
      "106643285105852243468371/2102071041"
    ],
    [
      "363366677",
      "56704515982431"
    ],
    [
      "1353534905",
      "56255492437587"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Mestre construction: sextuple [-494, -490, -156, 308, 342, 490], T = 413; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x), p(x)=prod(x-a_i) on the locus sum a_i = 0, 12 p5 = 5 p2 p3. Found by Nagao-sum sieve + ratpoints search on the quartic.",
  "created_at": "2026-10-11 22:57:48",
  "updated_at": "2026-10-11 22:57:48"
}