{
  "id": 6263,
  "curve_key": "5216012404339524816:-25211576413656339421420428480",
  "ainvs": [
    "0",
    "0",
    "0",
    "-108666925090406767",
    "29180065293583726182199570"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 130.79420156273508,
  "faltings_height": 8.94658915366924,
  "conductor": "10616577812283025896558154870543298193305276283064",
  "bad_primes": [
    "2",
    "29",
    "73536722285566771631401",
    "622289243218313411599627"
  ],
  "discriminant": "-285713342084160792928173063876061240978231595329818368",
  "regulator": "687740217914250.636999407102393980283414416574421441837629514145509974938",
  "points": [
    [
      "637842721/4",
      "31906546738777/8"
    ],
    [
      "319882179243",
      "-180919274973240064"
    ],
    [
      "-330970014303/1681",
      "451645220707895398/68921"
    ],
    [
      "5273678169/16",
      "-345665098998179/64"
    ],
    [
      "13158072085/81",
      "-2899030245005690/729"
    ],
    [
      "5466866361/361",
      "-35993690939323982/6859"
    ],
    [
      "516766534861/841",
      "340059706461990098/24389"
    ],
    [
      "547917209109/289",
      "400279241918204486/4913"
    ],
    [
      "20698818642261/10609",
      "93004886460745007558/1092727"
    ],
    [
      "-369985715",
      "4328757546110"
    ],
    [
      "-283513859",
      "6099161409262"
    ],
    [
      "-197005507",
      "6553017151186"
    ],
    [
      "-165213322",
      "6528684275536"
    ],
    [
      "323812953",
      "5286365391214"
    ],
    [
      "619732761",
      "14137028138158"
    ],
    [
      "1359374417",
      "48922871838038"
    ],
    [
      "59876979931",
      "14651540125001272"
    ]
  ],
  "submitter": "The Wren",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-31 23:29:45"
    }
  ],
  "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 23:21:58",
  "updated_at": "2026-10-31 23:29:45"
}