{
  "id": 6266,
  "curve_key": "8177492843464264928976:-701381029362270740150348034843840",
  "ainvs": [
    "0",
    "0",
    "0",
    "-170364434238838852687",
    "811783598798924467766606521810"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 151.36701767446618,
  "faltings_height": 10.554864391076336,
  "conductor": "11263947205505276370500249815376820412893317391816209656",
  "bad_primes": [
    "2",
    "7",
    "257",
    "272110933",
    "620856747239",
    "4632677404619479303670913721139"
  ],
  "discriminant": "31773702723599859754750960687209027078942682284991702316353792",
  "regulator": "137731480853551159.69095932309382511634141121225614553538655681286432016698",
  "points": [
    [
      "23210033101",
      "-3059574332630582"
    ],
    [
      "-11897904495",
      "1074474031027250"
    ],
    [
      "278455081273/16",
      "-113010434425226989/64"
    ],
    [
      "1391756770717/121",
      "-813923822298045578/1331"
    ],
    [
      "12277062089071/1369",
      "-3652723704515219152/50653"
    ],
    [
      "8733084990937/841",
      "9829259832144645382/24389"
    ],
    [
      "36801183951355/3481",
      "90061895272441627640/205379"
    ],
    [
      "12957453973",
      "883059435837026"
    ],
    [
      "66446041387459/5041",
      "331198969256623656104/357911"
    ],
    [
      "-8510633531",
      "1282676951901646"
    ],
    [
      "-2370317167",
      "1096487092363726"
    ],
    [
      "3473035313",
      "511853069977774"
    ],
    [
      "6075947443",
      "31061815320424"
    ],
    [
      "9975816913",
      "324070669381774"
    ],
    [
      "11654468342",
      "639737352281888"
    ],
    [
      "18167001257",
      "1926813072375562"
    ],
    [
      "18446529877",
      "1986462697477538"
    ],
    [
      "52180062945/4",
      "7196794722093305/8"
    ]
  ],
  "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 23:26:36",
  "updated_at": "2026-10-31 23:26:36"
}