{
  "id": 6252,
  "curve_key": "1909297851202089:-1646116435357505131569237",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-39777038566710",
    "1905227365682112803216"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 111.52092213996086,
  "faltings_height": 7.351230996189592,
  "conductor": "1930969314026470623366215581134549103384590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "24821",
    "40127",
    "32469846454211",
    "663432375663989923"
  ],
  "discriminant": "-1564085144361441204926634620718984773741517900",
  "regulator": "97846278285603.90392612413783800877315912887905724522472778765913834335",
  "points": [
    [
      "-101160782/121",
      "-58592146576924/1331"
    ],
    [
      "30270406318",
      "-5266579137440264"
    ],
    [
      "2781828352/289",
      "-241421834401132/4913"
    ],
    [
      "177563532943/11236",
      "-86086622666668409/1191016"
    ],
    [
      "562843003/961",
      "1292430290237416/29791"
    ],
    [
      "-57695486018/4489",
      "5153121974622718/300763"
    ],
    [
      "-309224726/25",
      "-2807902104028/125"
    ],
    [
      "28632999167977/153664",
      "153143808602141561273/60236288"
    ],
    [
      "216869570101/625",
      "100977455769423274/15625"
    ],
    [
      "-12417920",
      "22012418164"
    ],
    [
      "3321082",
      "42539551348"
    ],
    [
      "42274147/4",
      "412968835013/8"
    ],
    [
      "14997376",
      "68416949452"
    ],
    [
      "28477063",
      "154471268101"
    ],
    [
      "29629850",
      "163507398546"
    ],
    [
      "-118524266/25",
      "5572615256192/125"
    ]
  ],
  "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 22:53:49",
  "updated_at": "2026-10-31 22:53:49"
}