{
  "id": 6257,
  "curve_key": "106122338054904496:-34578009654953427037201760",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-2210882042810510",
    "40020845245008628896561"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 117.61052030552416,
  "faltings_height": 7.519769437465414,
  "conductor": "326491505507877704753301865214116989688788",
  "bad_primes": [
    "2",
    "3",
    "73",
    "372707198068353544238929069879128983663"
  ],
  "discriminant": "-286006558824900869363892433927566482967378288",
  "regulator": "6960818758360.330257427841600636257534331898247935265720605420026347990",
  "points": [
    [
      "286183978",
      "-4779762837907"
    ],
    [
      "124632690",
      "-1304005575669"
    ],
    [
      "689155949/100",
      "158466794598057/1000"
    ],
    [
      "1342811702/121",
      "172784474661195/1331"
    ],
    [
      "85175197/4",
      "407758847039/8"
    ],
    [
      "2752719792/169",
      "-200527103467101/2197"
    ],
    [
      "38296873382/1849",
      "-4436776247332869/79507"
    ],
    [
      "59863620140/2209",
      "301857604673637/103823"
    ],
    [
      "157225987025/3136",
      "41259659907732729/175616"
    ],
    [
      "-29320954",
      "282202503639"
    ],
    [
      "13008912",
      "116022397065"
    ],
    [
      "19963914",
      "61965803187"
    ],
    [
      "25827128",
      "12159461007"
    ],
    [
      "28730411",
      "14711390919"
    ],
    [
      "108472021/4",
      "23104264429/8"
    ],
    [
      "435567449/16",
      "189231932907/64"
    ]
  ],
  "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 23:06:16",
  "updated_at": "2026-10-31 23:06:16"
}