{
  "id": 451,
  "curve_key": "6015099816575162120817713772909361:-445648195436796032922854409609658749131935738361641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-125314579511982544183702370268945",
    "515796522496291694328940607345967092483061434025"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 233.3387430381054,
  "faltings_height": 17.378957431146812,
  "conductor": "19743833636741367656282934696071380406607013504205890312077895145804538615210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "53",
    "2687",
    "9027637",
    "138019411",
    "373691037405163133",
    "4082768862599049033340737349096117"
  ],
  "discriminant": "11014220843264556546447448734799935278705945925559546130402155148854354537539562363089294950400000",
  "regulator": "123367931048025372478.073048759299172440538915524437839107849804032657462050317",
  "points": [
    [
      "10635368900033490",
      "-621295196351031348699645"
    ],
    [
      "22943999582720010",
      "3117518619081170241383835"
    ],
    [
      "-3759864604925265/4",
      "6363684426942023702464065/8"
    ],
    [
      "8014563762558570",
      "162037555206235925526075"
    ],
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      "5001305407997940",
      "118987263395518717539105"
    ],
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      "125197160910015690",
      "44127182823092593448348955"
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      "68669164470090",
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      "-9331806730053910",
      "934114456430677340551355"
    ],
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      "27595969394288490",
      "4251233395942110140075355"
    ],
    [
      "39494525707686090",
      "-7561138254014203156937445"
    ],
    [
      "137682676126364826",
      "-50923928215193560374009813"
    ],
    [
      "8271383322488250",
      "212520014320607662366155"
    ],
    [
      "-11714068234196430",
      "-613467765336802272443925"
    ],
    [
      "2894678309835210",
      "421077316002349750756635"
    ],
    [
      "127646469230866770",
      "45435041899537238972756355"
    ],
    [
      "7565030616363690",
      "-27059852451236779584645"
    ],
    [
      "7562757388226250",
      "25038624217646470637595"
    ],
    [
      "4982155776332490",
      "122988696623149476995355"
    ],
    [
      "1188059119004370",
      "607118044401419029846275"
    ],
    [
      "-173832201139235190/49",
      "328226801747061958228499565/343"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -10/7. 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 15:55:03",
  "updated_at": "2026-08-30 15:55:03"
}