{
  "id": 428,
  "curve_key": "1196027469149895038464683540230078800:-1319732504648202390850297388731953328028801784339198400",
  "ainvs": [
    "0",
    "1",
    "0",
    "-24917238940622813301347573754793308",
    "1527468176676160166289505293787711918102662665461488"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 249.23404817949415,
  "faltings_height": 18.629408377876704,
  "conductor": "446480526610737179355955961227189254020824567046961876711405982701219954637800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "31",
    "47",
    "61",
    "73",
    "101",
    "11939",
    "5568285957643",
    "2437788650277983056207690736085794602381810177"
  ],
  "discriminant": "-17823187605965034199768344802638363317494960253584381536607303619622147560661226461773809327050839520000",
  "regulator": "341674714485273844622.94545361261494334321481368766421980681514238687641058712867",
  "points": [
    [
      "57933032599511022",
      "-16684540924439275616791062"
    ],
    [
      "85950447340642068",
      "4558234550645150694659340"
    ],
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    ],
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      "-41955010236825509981882340"
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      "-144408146282779272",
      "-45981240376955693077574460"
    ],
    [
      "27286357460584744398",
      "142531578686178878956461958410"
    ],
    [
      "327051983255582397/4",
      "48504699838226895801382845/8"
    ],
    [
      "34875168603019698",
      "26474386609952499427118910"
    ],
    [
      "122574460162343142",
      "-17744600056793831151232302"
    ],
    [
      "1160916650133925638",
      "-1239838654304331011218898610"
    ],
    [
      "109299386386024788",
      "10476574609858392308413140"
    ],
    [
      "90800630131556298",
      "-3687285920663102227560090"
    ],
    [
      "175670270818256343",
      "50709391236220297036310910"
    ],
    [
      "186733496773008138",
      "58188227253028711539811110"
    ],
    [
      "41092139179916778",
      "-23936420556125255023135290"
    ],
    [
      "83509732602785442",
      "5387270987570753075196402"
    ],
    [
      "105704389646328888",
      "8642104589468300324464860"
    ],
    [
      "104620427215829478",
      "8107524463592025313631790"
    ],
    [
      "153798722176767348",
      "36512886240471431017658340"
    ],
    [
      "189459276261035448",
      "-60060571420582630886042340"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 13/6. The 4 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 >= 21.",
  "created_at": "2026-08-30 01:39:34",
  "updated_at": "2026-08-30 01:39:34"
}