{
  "id": 462,
  "curve_key": "279900917906157255683521267269892561:-115710591494870427755844967123141573929001046785180441",
  "ainvs": [
    "1",
    "0",
    "0",
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    "133924295711655587194437025768409363893193455880025"
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  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 244.8592312341811,
  "faltings_height": 18.417976956568076,
  "conductor": "185825674244197562991939767988017108291227572248603957165920198900856248993890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "41",
    "109",
    "557656420008563",
    "2792657071781563542343",
    "45070114994698512690168645973549"
  ],
  "discriminant": "4941992565371643620810087164829754113722511270106186147330892577260865813848839664661473374681600000000",
  "regulator": "168096208662763960510.892493175875190472772459429509476031134792547891704698269",
  "points": [
    [
      "81994795736121090",
      "14389357183593365506103205"
    ],
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      "5194338555763404445088325"
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      "3002734786820423758458380205"
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      "594748118308858614/25",
      "367912189195286588035045977/125"
    ],
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      "296103931252848735/4",
      "-83103738215046850691336235/8"
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      "-81275952408710874",
      "-8424675073539321827453043"
    ],
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      "76687090186005030",
      "-11735889219566931404833395"
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      "64654840840903590",
      "5213234711425779425048205"
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      "13089879709325670",
      "-7735410088313394039061875"
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      "-33053018863096410",
      "17045669641615903274648205"
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      "60197740356770150",
      "-1018681973554748129450995"
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    [
      "-85889992228344690",
      "-1074098136462964401309315"
    ],
    [
      "-85682174929833660",
      "-2128377329845640170635795"
    ],
    [
      "60860515824480870",
      "2111337181981886085512205"
    ],
    [
      "-81152299857542910",
      "-8526478603122817094960295"
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      "20668073488375590",
      "4715078211635330525648205"
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    [
      "-6044247061084410",
      "-12998042655830195586051795"
    ],
    [
      "-44030040743680260",
      "-17473314403055424696393795"
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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 = -34. 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 20:00:34",
  "updated_at": "2026-08-30 20:00:34"
}