{
  "id": 436,
  "curve_key": "4111789722159570872947690339616721601:-8039860487821888780348156801722375047532182408320738849",
  "ainvs": [
    "1",
    "0",
    "0",
    "-85662285878324393186410215408681700",
    "9305394083127186081227398401022012428368804281129232"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 252.92076521107148,
  "faltings_height": 18.99998622216982,
  "conductor": "6659238930698749498275990668738524591136206467171330889159250348722050046602270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "31",
    "37",
    "59",
    "103079",
    "209563",
    "18283322059798488583734807181",
    "17266444769512957737328281593489"
  ],
  "discriminant": "2822864776306595502439005729534366424563694178962993624011022240824211533040745014935144313124315136000000",
  "regulator": "1433381768151416253076.2629708056391346889888746960591966158829737841285685991987",
  "points": [
    [
      "19660969398442454",
      "-87342947765714641544049352"
    ],
    [
      "126230456546659724",
      "22440519097163676329067368"
    ],
    [
      "131002798560820698496/9",
      "-1499110697604577069716267657524/27"
    ],
    [
      "98378199767480264",
      "42781110368327024090054108"
    ],
    [
      "559580290955541704",
      "369583414967705630468173148"
    ],
    [
      "-315097468016618296",
      "70798769197812717138253148"
    ],
    [
      "-327632986045763758",
      "46924989136515278595874598"
    ],
    [
      "-228449681979907046",
      "130200986440534461509512648"
    ],
    [
      "40767921013277924",
      "-76686882970817902091584432"
    ],
    [
      "439744618535145434",
      "238058029208386291778819528"
    ],
    [
      "137114545559485454",
      "-11732723292791646668908102"
    ],
    [
      "-260774407515264886",
      "117942392210068970890249928"
    ],
    [
      "285333492306937832",
      "89964208074208568844879068"
    ],
    [
      "194896930779094184",
      "3633328137141890322093788"
    ],
    [
      "291506410111396424",
      "-95421871855010947969040932"
    ],
    [
      "-162442291570020536",
      "137601331628938628483225308"
    ],
    [
      "218546663542383752",
      "31977395547165784894000028"
    ],
    [
      "-3577960748916764/9",
      "2609302290046655971258552196/27"
    ],
    [
      "-8815399344098714/9",
      "-2616256587078778253489116954/27"
    ],
    [
      "1825648433065214",
      "95650462360816657379674808"
    ],
    [
      "3595676155373384",
      "-94854766526577549919192612"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [
    {
      "kind": "rank_improved",
      "user": "Jason Ma",
      "old_rank": 20,
      "new_rank": 21,
      "at": "2026-09-03 16:32:54"
    }
  ],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 39. 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 04:29:52",
  "updated_at": "2026-09-03 16:32:54"
}