{
  "id": 161,
  "curve_key": "8933722659848225280802461489:-835302206420233693598092411083230386007337",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-186119222080171360016717948",
    "966784961134576267766275148260409718847"
  ],
  "rank_lower_bound": 18,
  "naive_height": 193.07889207019377,
  "faltings_height": 13.95834148292453,
  "conductor": "15293463740752553768990420489911754342865071901048558390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "23",
    "31",
    "37",
    "157",
    "163",
    "259627",
    "39576820317654329",
    "99173840155499332801"
  ],
  "discriminant": "8844410691059589836574217469287328213356255539746089974415484198645460595507200",
  "regulator": "1720477128584811.6188214221553592298019361587306052672826796241020503339218",
  "points": [
    [
      "-13832435464763",
      "-29910199873434594523"
    ],
    [
      "-15238574724275",
      "16259276081044689533"
    ],
    [
      "7127974835053",
      "1513322317013240093"
    ],
    [
      "8923742719093",
      "4065823273255454213"
    ],
    [
      "-15682513924187",
      "5350268149265678453"
    ],
    [
      "2246837286493",
      "-23663221783492721707"
    ],
    [
      "7005303109877",
      "2596829909785016837"
    ],
    [
      "158755543668949/25",
      "800012588152647945433/125"
    ],
    [
      "-10537945303307",
      "-41927054304229542907"
    ],
    [
      "267554946135157/49",
      "3651231326520682150499/343"
    ],
    [
      "86871401366965",
      "800240902996342804421"
    ],
    [
      "-14940295804037",
      "-20312583017768395267"
    ],
    [
      "6964686011653",
      "2891018295500550053"
    ],
    [
      "-13822405039787",
      "-29975099320903870267"
    ],
    [
      "9021833770315",
      "-4686876167691073129"
    ],
    [
      "-9560836755947",
      "43269950494397842853"
    ],
    [
      "9269843446837",
      "6168182658272383877"
    ],
    [
      "473703694901557/49",
      "-2890170815217234366301/343"
    ]
  ],
  "submitter": "cocoxhuang",
  "commentary": "New curve of rank ≥ 18 and log conductor 127.067, found as the specialization t = 17142/23 of the 2-parameter Mestre rank-12 family over Q(t) used by Fermigier in 'Une courbe elliptique définie sur Q de rang ≥ 22' (Acta Arith. 82 (1997)) — here at family parameters (u,v) = (2,5), sextuple {348, −600, −216, 492, 876, −900} — located by a discriminant-gated exhaustive specialization scan crossed with a staged Nagao-sum sieve; 18 independent points certified by positive-definite Néron–Tate height pairing. Conductor N (log N ≈ 127.07) is squarefree apart from 3², with bad primes 2, 3², 5, 13, 19, 23, 31, 37, 157, 163, 259627, 39576820317654329, 99173840155499332801.",
  "created_at": "2026-06-25 02:54:38",
  "updated_at": "2026-07-01 22:32:42"
}