{
  "id": 3642,
  "curve_key": "1288549699935213637220429041:-45859764365757300394913998739967799996105",
  "ainvs": [
    "1",
    "0",
    "0",
    "-26844785415316950775425605",
    "53078430978883527280513999906842557121"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 187.26994449941486,
  "faltings_height": 13.464133673984312,
  "conductor": "52730095526316529723237209878616107447931486",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "23",
    "31",
    "37",
    "43",
    "53",
    "59",
    "73",
    "211",
    "601",
    "36697",
    "78193",
    "10736721060361"
  ],
  "discriminant": "21029407578843431715833967440221498961177210955277982484181090108410515423232",
  "regulator": "13120789678363475.4055177731366404580001704564904550327069841448697",
  "points": [
    [
      "2744993348530",
      "270492323384302471"
    ],
    [
      "3588059963734",
      "1717857507293552395"
    ],
    [
      "-6892997802664256690/1164241",
      "2658434546377179804569101001/1256216039"
    ],
    [
      "-20170153738118276/6241",
      "5078073203933881759673545/493039"
    ],
    [
      "-130923827481359/64",
      "5105479194265758846155/512"
    ],
    [
      "10957461718429/16",
      "378711332743068346099/64"
    ],
    [
      "43942428668157586/5041",
      "7853225112404850818324321/357911"
    ],
    [
      "52105349524128538/19321",
      "1462089790391458907311597/2685619"
    ],
    [
      "274976860125142750/127449",
      "103784034551569266067708723/45499293"
    ],
    [
      "954201995338712866/290521",
      "91233583613669663732249909/156590819"
    ],
    [
      "1080022111679406876/326041",
      "131932424921627117587421973/186169411"
    ],
    [
      "113167514087470352530/52171729",
      "847216983197427929671718419793/376836398567"
    ],
    [
      "163452520385516912530/707281",
      "2089195959565796959709499352879/594823321"
    ],
    [
      "3016743851994613779682/927994369",
      "11482631822057360799205984302361/28269492462847"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -60/91, u = 2/5 of the Elkies-Klagsbrun family y^2 = x^3 + 2A(t,u)x^2 + B(t,u)x (arXiv:2003.00077, Sec. 9, eqs. (3)-(4)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:25:25",
  "updated_at": "2026-09-29 19:25:25"
}