{
  "id": 94,
  "curve_key": "2532074705548254150979223648161:-4022653388419864861626256258360328558188935409",
  "ainvs": [
    "1",
    "0",
    "0",
    "-52751556365588628145400492670",
    "4655848829189654008696988351827664455270212"
  ],
  "rank_lower_bound": 18,
  "naive_height": 210.01977539468692,
  "faltings_height": 15.292901227127402,
  "conductor": "42682665107572966519161676237698352985292192192557605656213390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "31",
    "43",
    "47",
    "79",
    "9993701",
    "10586665361105868350008239735615374993841941"
  ],
  "discriminant": "30329481606266546964270732939527654191747398716945306980836010472365688288267827200000",
  "regulator": "65246279290282792.166077869689225539534770704132049918615908028178898997037",
  "points": [
    [
      "200212896884244",
      "-1455981468425261901102"
    ],
    [
      "128196315395964",
      "-10477319710847678382"
    ],
    [
      "-205036993618356",
      "-2617647609254374848702"
    ],
    [
      "105878869571004",
      "507455632507918359858"
    ],
    [
      "144206806357572",
      "-218135007877172188782"
    ],
    [
      "781870376871564",
      "-21009164439672659945982"
    ],
    [
      "126484045207764",
      "-84483037515959599782"
    ],
    [
      "-9476651858696364/49",
      "-947083054999256026387626/343"
    ],
    [
      "18548018008764",
      "-1919321000484069899982"
    ],
    [
      "141801409967604",
      "163998231164818681938"
    ],
    [
      "592900127539964",
      "13483395378366317086418"
    ],
    [
      "196304908050924",
      "1365719545267889883378"
    ],
    [
      "19275260524764",
      "1909505236219745647218"
    ],
    [
      "128085575458524",
      "22279824368584248498"
    ],
    [
      "7388129939825436/49",
      "123606160234861151139774/343"
    ],
    [
      "124886954998764",
      "-125293276775632768782"
    ],
    [
      "127624354397784",
      "46988285799809697078"
    ],
    [
      "1001741371622664",
      "-30936154910786659336782"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "New curve of rank >= 18, found as the specialization T = 1315/12 of the 2-parameter Mestre rank-12 family over Q(t) used by Fermigier (Acta Arith. 82 (1997), sextuple {0,55,314,378,1007,1036}), located by a staged Nagao-sum sieve; submitted for its small conductor at this rank. 18 independent points certified by positive-definite Neron-Tate height pairing.",
  "created_at": "2026-06-12 02:09:41",
  "updated_at": "2026-07-01 22:33:40"
}