{
  "id": 6267,
  "curve_key": "8438123720449282398681:-798456462720993431112951666301725",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-175794244176026716639",
    "924139424489542810017330367009"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 151.52046646431805,
  "faltings_height": 10.540024777211443,
  "conductor": "795674228819300344739553923797214936788267268052782",
  "bad_primes": [
    "2",
    "7",
    "19",
    "31",
    "71",
    "425811887",
    "167981800022770708746362587734947359"
  ],
  "discriminant": "-21251164451029323090294950562147074296848045520718025039649028",
  "regulator": "152686520701706326.11916240557590408344504518295497096377255842563931966858",
  "points": [
    [
      "1084296139136",
      "1128988049709794799"
    ],
    [
      "1718273689812",
      "-2252297661457811437"
    ],
    [
      "1695371666989/9",
      "2202158722087378138/27"
    ],
    [
      "16940901090960/289",
      "-68084728724874009169/4913"
    ],
    [
      "4783732418605/144",
      "-9736191350229775361/1728"
    ],
    [
      "69289682205414/4489",
      "413283019807066511077/300763"
    ],
    [
      "46291924693174/7569",
      "183617934300521489257/658503"
    ],
    [
      "1898838730537/576",
      "-8526673033363930025/13824"
    ],
    [
      "28270341257004/9409",
      "-593639898628534672103/912673"
    ],
    [
      "-3468073700",
      "1221514910738297"
    ],
    [
      "-727047972",
      "1025459263994795"
    ],
    [
      "5878674200",
      "306366647115697"
    ],
    [
      "8123367343",
      "179305385056427"
    ],
    [
      "28115475136",
      "4266872380988049"
    ],
    [
      "-17700175556/25",
      "127980027937041343/125"
    ],
    [
      "549328287809/64",
      "111703513763142693/512"
    ],
    [
      "596004090640/169",
      "1296107556717154251/2197"
    ],
    [
      "220758139722470/22201",
      "1320217993764635493087/3307949"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 18 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_18.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 23:27:54",
  "updated_at": "2026-10-31 23:27:54"
}