{
  "id": 458,
  "curve_key": "1174063066704423327414361040523444961:-1275148323975435256883626421627428057827995806114457041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-24459647223008819321132521677571770",
    "1475866115712309323058485904595825308688025746908900"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 249.165315052105,
  "faltings_height": 18.56943017187508,
  "conductor": "127539526964771188715253520186359953250470657797397956136339909486451272206611990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "83",
    "97",
    "5541979",
    "13598052927397543826778726821571445157012029493876346741264068411"
  ],
  "discriminant": "-4425023236897122347983043266683538093006074579543760499341768527284100218962279072060350429538560000000",
  "regulator": "2255884186515467036914.3517382021156105599407290746853899506328130897926054055134",
  "points": [
    [
      "135790045638840660",
      "-25657621374695949238556490"
    ],
    [
      "23799517271612940",
      "-30120072569537908153436970"
    ],
    [
      "279755952459059052",
      "-128560430458044660320249538"
    ],
    [
      "69815632498409172",
      "-10416203940294171765134538"
    ],
    [
      "-543810692566283540/9",
      "-1411559441052274594044751190/27"
    ],
    [
      "29679615187438140",
      "-27857806188535086843001170"
    ],
    [
      "65083491858257940",
      "-12634535402978304980600970"
    ],
    [
      "108696330510912120",
      "10071129561251200638488850"
    ],
    [
      "21233015442698089020",
      "-97837594353090533745023348970"
    ],
    [
      "3642702655023805440",
      "6946108816893288784373695530"
    ],
    [
      "23361806407705140",
      "30285224751988812341791830"
    ],
    [
      "61946169258468900",
      "14085184793774728314043830"
    ],
    [
      "-174803064575155950",
      "20253036826296762282908580"
    ],
    [
      "296778477490662435/4",
      "-66703654440583699926003885/8"
    ],
    [
      "97900766121927990",
      "4425345266394687227887530"
    ],
    [
      "90364581538404240",
      "-1864295619901145456962470"
    ],
    [
      "196795348131855540",
      "-65451448257662630973846570"
    ],
    [
      "359795922537300",
      "-38302293416520773909957130"
    ],
    [
      "-1033073548019628",
      "38744465769370427027570166"
    ],
    [
      "-1437242866184520",
      "38871809841884083084297590"
    ],
    [
      "-1463681124897708",
      "38880124793983528544083446"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [
    {
      "kind": "rank_improved",
      "user": "Jason Ma",
      "old_rank": 20,
      "new_rank": 21,
      "at": "2026-09-03 16:33:17"
    }
  ],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -40/9. The 3 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 20.",
  "created_at": "2026-08-30 15:56:56",
  "updated_at": "2026-09-03 16:33:17"
}