{
  "id": 6259,
  "curve_key": "3105322482117124521:-5395102163804532285279475605",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-64694218377440094",
    "6244331224280652146766824"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 127.73894772858064,
  "faltings_height": 8.525175667119633,
  "conductor": "21839804528723346103136677719886089956839385598",
  "bad_primes": [
    "2",
    "3",
    "137",
    "43261087",
    "204719045132382640207417557922377169"
  ],
  "discriminant": "484712621710485943413015425315151880502093323962012",
  "regulator": "11775561594857074.0451397073963289376140394931292631251562018659993037209",
  "points": [
    [
      "-20504129",
      "2749957431820"
    ],
    [
      "43055498233",
      "-8933803873288610"
    ],
    [
      "-5215276459/25",
      "-408142202753926/125"
    ],
    [
      "183220625",
      "-736091161607"
    ],
    [
      "8647017838/49",
      "-195059549343980/343"
    ],
    [
      "17763741241/1681",
      "-162540922048881250/68921"
    ],
    [
      "55463093566/529",
      "-9534214253469244/12167"
    ],
    [
      "1752213424483/10609",
      "277836090006680080/1092727"
    ],
    [
      "13462694602/81",
      "210104724736000/729"
    ],
    [
      "-123585532",
      "3514607475480"
    ],
    [
      "-94398332",
      "3392711304280"
    ],
    [
      "-18888317",
      "2731228470877"
    ],
    [
      "132161860",
      "51529500292"
    ],
    [
      "172119652",
      "456268617928"
    ],
    [
      "211543750",
      "1423065626518"
    ],
    [
      "8410958713/64",
      "56016795542225/512"
    ],
    [
      "243019371265/1849",
      "8644106675786794/79507"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 17 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_17.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 23:15:51",
  "updated_at": "2026-10-31 23:15:51"
}