{
  "id": 4179,
  "curve_key": "5378990703288668457769:-365227480428634526307225833091797",
  "ainvs": [
    "1",
    "1",
    "0",
    "-112062306318513926203",
    "422716991190152888926575022753"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 150.11036312349017,
  "faltings_height": 10.46811875360961,
  "conductor": "284098332150954535104446062634390597697230108860266690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "37",
    "2150793641842338822806011527249531362686275333941"
  ],
  "discriminant": "12871606201980117497887574181788192339090703902217951089160300",
  "regulator": "20703650039958719.9109671420581607047404250667051614815127891469886705359",
  "points": [
    [
      "34416185164/9",
      "-6043927238420693/27"
    ],
    [
      "28039679056/9",
      "-8699965315582939/27"
    ],
    [
      "-57224957478671/20736",
      "-2517725523162991709233/2985984"
    ],
    [
      "-13206195460096579/1125721",
      "-418618654622388686380769/1194389981"
    ],
    [
      "-10196057761688693/1868689",
      "2385039517144374747209951/2554497863"
    ],
    [
      "-2039706779003/169",
      "-287527163413701056/2197"
    ],
    [
      "-227151683803274/54289",
      "11442946414935774453791/12649337"
    ],
    [
      "82625389",
      "643007239842163"
    ],
    [
      "1513573713237259/366025",
      "38374453957038032279813/221445125"
    ],
    [
      "5002302935013484/1100401",
      "98185021278866773395257/1154320649"
    ],
    [
      "15950588579",
      "1641158179514993"
    ],
    [
      "885942921469/16",
      "-819567271166800703/64"
    ],
    [
      "366496363464886/9",
      "-7016241417218312371819/27"
    ],
    [
      "8791037975966968/564001",
      "664721466849191254916335/423564751"
    ],
    [
      "144234631237316/18769",
      "318780886489690745539/2571353"
    ],
    [
      "67335971851334/9025",
      "-37871202821517890063/857375"
    ],
    [
      "6084748851381/16",
      "-15003676380061137833/64"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Mestre construction: sextuple [-1053, -495, 8, 39, 456, 1045], T = 153; 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 a discriminant-first sweep + Nagao-sum rescoring + ratpoints search on the quartic.",
  "created_at": "2026-10-11 22:59:07",
  "updated_at": "2026-10-11 22:59:07"
}