{
  "id": 6256,
  "curve_key": "51559934631026241:-12628561932926400274436961",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1074165304813047",
    "14616391394613548743119"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 115.59600660105501,
  "faltings_height": 7.590077022435647,
  "conductor": "40531433402643104717643452250340307599810",
  "bad_primes": [
    "2",
    "5",
    "4053143340264310471764345225034030759981"
  ],
  "discriminant": "-12970058688845793509645904720108898431939200000",
  "regulator": "3149923833184.353219760490552206912179204011086616023532853791540037664",
  "points": [
    [
      "4216009983/169",
      "-127090566061018/2197"
    ],
    [
      "151957383859",
      "-59235663718540818"
    ],
    [
      "5944152523/169",
      "-313428028238538/2197"
    ],
    [
      "17906711123/484",
      "-1701119523485957/10648"
    ],
    [
      "-261954463229/6889",
      "-12529943037771726/571787"
    ],
    [
      "-1786655953/49",
      "-24978963423266/343"
    ],
    [
      "-19661034323/841",
      "-4003623464424046/24389"
    ],
    [
      "124339818183/2209",
      "37788052188504598/103823"
    ],
    [
      "7804101104979/14641",
      "21760728444439072238/1771561"
    ],
    [
      "-21157693",
      "166959829886"
    ],
    [
      "2034777",
      "111529826586"
    ],
    [
      "15711427",
      "40217391486"
    ],
    [
      "17337627",
      "34697072286"
    ],
    [
      "24997277",
      "58168926136"
    ],
    [
      "26150067",
      "66387166046"
    ],
    [
      "151372843/9",
      "976149321322/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 16 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_16.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 23:04:15",
  "updated_at": "2026-10-31 23:04:15"
}