{
  "id": 457,
  "curve_key": "13189088658637085771463499964401397200:-47614548399413649981919363639651367748553027249313080000",
  "ainvs": [
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    "1",
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  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 256.4173596563161,
  "faltings_height": 19.21102460789509,
  "conductor": "4985496876385205151318529244550971267815315488413817176648366062065676226102431879800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "29",
    "293",
    "358987",
    "483914399",
    "208301526751570139",
    "131343899330485327769779455587343605984077"
  ],
  "discriminant": "15696711652466593784984814071054398908676862294563966753627506827350997270194814689646347027702776516000000",
  "regulator": "7831985639918254024867.9835468280953149474752781845151313384463365264286116879476",
  "points": [
    [
      "-520813263718905358",
      "-238633475489700629811325398"
    ],
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      "-355964894258908576",
      "-328350710833589068423906464"
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      "3009238818873955042/9",
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      "-2200100045164934443/4",
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    ],
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      "-1247328958626610811314566075600"
    ],
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      "597244387722017141/4",
      "-1055622143996426584998146727/8"
    ],
    [
      "1337485094080435778",
      "-1442285402105459163074391450"
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      "1279136750591221178",
      "1340354212476561094926794850"
    ],
    [
      "37190151245892097013/4",
      "-226446455320629343268220917529/8"
    ],
    [
      "528760140685323983",
      "240114978204363129039340350"
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    [
      "-296001634134098506",
      "332427176832647198134399266"
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    [
      "345196676059468214",
      "-37319006186174989582296354"
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    [
      "181525958194605278",
      "105889758856010865796747050"
    ],
    [
      "515781718147924",
      "-234451932024163349883754536"
    ],
    [
      "-2932477948987312",
      "-236463888630870654222583800"
    ],
    [
      "-3490491421050016",
      "-236787837894951553551571776"
    ],
    [
      "-69893442383372243/4",
      "-1958044709714095270442559525/8"
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  ],
  "submitter": "Bhavik Mehta",
  "history": [
    {
      "kind": "rank_improved",
      "user": "Jason Ma",
      "old_rank": 20,
      "new_rank": 21,
      "at": "2026-09-03 16:32:30"
    }
  ],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -31/18. 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 15:55:30",
  "updated_at": "2026-09-03 16:32:30"
}