{
  "id": 87,
  "curve_key": "6147262740489604521484573249:-476308965003899493361072044153708073135457",
  "ainvs": [
    "1",
    "1",
    "1",
    "-128067973760200094197595276",
    "551283524310015496401062930694209419949"
  ],
  "rank_lower_bound": 18,
  "naive_height": 191.95741323219502,
  "faltings_height": 13.868689199539636,
  "conductor": "264272322302981023294226801215719105908812968488670879510837270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "70616456303529097632401",
    "44220273093899778186557524292644529"
  ],
  "discriminant": "3141026088650294736579116234013850169228851134468835623113068971509123596492800",
  "regulator": "94146143937784834.222309731780565912552858055405979898830305053693311440478",
  "points": [
    [
      "-12733690254771",
      "-10832050092834520535"
    ],
    [
      "7116342595149",
      "544176015111233065"
    ],
    [
      "5775628631469",
      "2067176413862584585"
    ],
    [
      "21771810757029",
      "89906083538801270665"
    ],
    [
      "5328143734701",
      "-4492244980411323575"
    ],
    [
      "7135632829749",
      "-874262666995103735"
    ],
    [
      "5162168706573",
      "-5266541863119888791"
    ],
    [
      "8183352551707",
      "7160640722003337311"
    ],
    [
      "10353533303901",
      "18307950595024354825"
    ],
    [
      "346395899469",
      "-22515836098862263415"
    ],
    [
      "7803676630173",
      "5206323527832720217"
    ],
    [
      "-2691447716443",
      "-29605322946651800879"
    ],
    [
      "13890747713721",
      "-38112777466974057287"
    ],
    [
      "22058269995549",
      "-91973691550298533415"
    ],
    [
      "65965817063413/9",
      "-68106097920473546893/27"
    ],
    [
      "-10499801042931",
      "27173753106374947945"
    ],
    [
      "-12769843462147",
      "-10214059849860638471"
    ],
    [
      "22805787632961",
      "-97426767137009707655"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "New curve of rank >= 18 and naive height 191.96, found as the specialization T = 679/26 (t = 679/52) of the 2-parameter Mestre rank-12 family over Q(t) used by Fermigier in 'Une courbe elliptique definie sur Q de rang >= 22' (Acta Arith. 82 (1997), sextuple {0,55,314,378,1007,1036}), located by a staged Nagao-sum sieve over ~1.9M specializations; 18 independent points certified by positive-definite Neron-Tate height pairing.",
  "created_at": "2026-06-11 15:35:46",
  "updated_at": "2026-07-01 22:32:41"
}