{
  "id": 446,
  "curve_key": "64444850348518977473589806826179001:-16329209082723320515316943286673191691864980943512749",
  "ainvs": [
    "1",
    "-1",
    "0",
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    "18899547549448287969118946591445127688679527385785"
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  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 240.45335368049825,
  "faltings_height": 17.834797200670167,
  "conductor": "183952363112619117727161581895997057816804962203234710810829751629070049712735430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "31",
    "53",
    "3823",
    "17109342568432627963608764579019760941917593271475015922815034559497"
  ],
  "discriminant": "581791133919543550001667862947405806718057189108956771493903914454372247222058213821114575018562500",
  "regulator": "586543816754491659578.067593519880199813388290721515160912493138812046098599578",
  "points": [
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      "6764955446141926",
      "-3182217296658307240099283"
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      "2003976391231864291985317"
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      "62009815027246951",
      "13194177081020317174063417"
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    [
      "350420811668446189/16",
      "-831648405591472255002557/64"
    ],
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      "-733279877941383395629523"
    ],
    [
      "547498844308553104/25",
      "781919721788556801760607/125"
    ],
    [
      "-22651368712180604",
      "6139155706478948292118177"
    ],
    [
      "90997381215139861",
      "25499653118422829418317872"
    ],
    [
      "-338087505843687776/25",
      "-735091054485035936042297503/125"
    ],
    [
      "27838953445263721",
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    [
      "31889608046342596",
      "-2917973765387700154600223"
    ],
    [
      "19117669718044216",
      "468370888484583743869837"
    ],
    [
      "18375899748819646",
      "-658105757499208763050823"
    ],
    [
      "142322120153682679/4",
      "32172654805876026554084711/8"
    ],
    [
      "1891989726690922969/64",
      "1149960600610241969357246999/512"
    ],
    [
      "-10616226935504729",
      "-5653000155283528048450823"
    ],
    [
      "555424990659573859/25",
      "-24103322642957122895953183/125"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 19/4. 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 15:54:59",
  "updated_at": "2026-08-30 15:54:59"
}