{
  "id": 438,
  "curve_key": "1278911034763315575244411535683310416:-1439369671582244407755570980997644214870846023355620800",
  "ainvs": [
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    "1",
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  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 249.4172169285881,
  "faltings_height": 18.618906396110578,
  "conductor": "223243626275999515172429388531596142565523604425645085402859340457191045183972568",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
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    "103",
    "149",
    "647",
    "104991636693989279044111798626139",
    "1273365940972077825163424690885798801"
  ],
  "discriminant": "11585080412284289954378843599464712400986297972622037795687456741862452941298011926641465790911858892032",
  "regulator": "345013985575145571017.355626299711263409382341193242242083691497848470950549137",
  "points": [
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      "-164502807167951642",
      "-39966330694450421407394430"
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    [
      "2147244483197250606/25",
      "-416554381327857398381656446/125"
    ],
    [
      "80221928840917747",
      "-6691675895819757910892916"
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    [
      "1261500295989278410",
      "-1405554933139492845734242218"
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    [
      "39640196021838334",
      "-25923984331172680864803978"
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    [
      "83113969652002942",
      "5059232193271654973748726"
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      "116573938674919882",
      "12005124766801714759274154"
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      "-85076315935621517",
      "57592778517514063581692220"
    ],
    [
      "-127041526905699341",
      "54776235618978018267694572"
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  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 3/10. 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 04:29:53",
  "updated_at": "2026-08-30 04:29:53"
}