{
  "id": 195,
  "curve_key": "2612721184108241595489:-155993673871847613487707706193937",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-54431691335588366573",
    "180548233661579697703929158997"
  ],
  "rank_lower_bound": 14,
  "naive_height": 148.2547364882902,
  "faltings_height": 10.344882362862343,
  "conductor": "4372904911177417822247776105333672098390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "97",
    "101",
    "260763461711492729725756564097"
  ],
  "discriminant": "-3760865945124333458688931654370706160938454707422168471961600",
  "regulator": "249748452478.896612615657083847531400376102137891106663850206439465",
  "points": [
    [
      "207486257967/49",
      "-55292996762624536/343"
    ],
    [
      "5474933974027/1089",
      "-6623280826452051464/35937"
    ],
    [
      "3485922442500407/683929",
      "-106607557059189060962616/565609283"
    ],
    [
      "1698397246847/289",
      "-1239319603387616376/4913"
    ],
    [
      "6268503683",
      "-292677744446952"
    ],
    [
      "6886225535",
      "-363685789290072"
    ],
    [
      "227040190559/25",
      "-82465709962026408/125"
    ],
    [
      "13210232763",
      "-1329222140213832"
    ],
    [
      "633401232898343/44521",
      "-14202660571046573935992/9393931"
    ],
    [
      "137061348627",
      "-50670858651120040"
    ],
    [
      "322490875343",
      "183089421925893528"
    ],
    [
      "85458871823",
      "24892801911837528"
    ],
    [
      "19817742035",
      "2623939877550036"
    ],
    [
      "18737544623",
      "2395674470375448"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥14. Mestre–Fermigier construction from the integer 6-tuple a=[-110, 6, 60, 44, 94, -94] with shift t=491/4: let p6(x)=∏(x−a_i) and q(x)=p6(x−t)·p6(x+t); completing q to g(x)²−r(x) gives the genus-1 quartic model y²=r(x), whose x=a_i±t base points plus a few small-x extra points supply 14 independent rational points. The shift t was selected by a Nagao–Mestre prime-sum sieve; the witness points were found by an integer quartic-point search and certified independent via the Néron–Tate height-pairing matrix.",
  "created_at": "2026-06-25 16:03:18",
  "updated_at": "2026-07-01 22:44:38"
}