{
  "id": 463,
  "curve_key": "224767015244996961110535726690796321:-102522804950390786655352803830283419514358833727096369",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4682646150937436689802827639391590",
    "118660653877767113794215602966189789176568569086692"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 244.20111734016012,
  "faltings_height": 18.276174936201812,
  "conductor": "246487897243725896044435022343614140294003013883226125048980054731003325130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "31",
    "47",
    "193",
    "1489657069",
    "12380920864241",
    "130895646239455408856934499736976436958033"
  ],
  "discriminant": "488629359416104574728554950607882050032668228093550025226917655718646710468793242267356967557120000000",
  "regulator": "40771069034647434994.0276133238166140394084724288500817109028367864395589160546",
  "points": [
    [
      "164176299210670604",
      "61441562939603718870044618"
    ],
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      "-78680401433729056",
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    ],
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      "425632816878281324",
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      "-5887861945466994790849942"
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      "113367005608299524",
      "32323438430883394379026538"
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      "11933568359799387106736138"
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      "31341011486411582",
      "-1639139334684609426874060"
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      "-78451812269454676",
      "1782243970464564934275338"
    ],
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      "-2216076320742076",
      "11358999604646376971160938"
    ],
    [
      "49840643780576324",
      "-3013832897969847239519662"
    ],
    [
      "31720873439863724",
      "-1428638856638953942326262"
    ],
    [
      "29767068272314412",
      "-2376543945011638064282230"
    ],
    [
      "27884629482322652",
      "-3125470544724181274454262"
    ],
    [
      "-2661406785133876",
      "-11450075506844375781267862"
    ],
    [
      "820750715440524908",
      "741052700466077860840215626"
    ],
    [
      "-74937472084620676",
      "-6981804759340349178092662"
    ],
    [
      "76596614912092652",
      "14470014540091465385105738"
    ],
    [
      "-1861606671197716",
      "-11285895960200648161424182"
    ],
    [
      "127727738994959324",
      "-40054402066749323240402662"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -39/16. 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 20:00:45",
  "updated_at": "2026-08-30 20:00:45"
}