{
  "id": 191,
  "curve_key": "2924316618320599734297591195298561:-157624488462778219456406517610332023994452455309441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-60923262881679161131199816568720",
    "182435750535622934108717118205361600171372294400"
  ],
  "rank_lower_bound": 16,
  "naive_height": 231.17510666228486,
  "faltings_height": 17.082959594776295,
  "conductor": "28964385051890469693884372342725226899763554916835745467259598596770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "37",
    "73",
    "5413",
    "33361703",
    "2721505543331",
    "57333637865117140073296578053387"
  ],
  "discriminant": "93858557525002069986716442228582690235767407598682422890314976013836608666063661484178636800000",
  "regulator": "4654554321845412.897032645881460013318440912154139638548237775729768145",
  "points": [
    [
      "948120211437022752",
      "-923167350663906647619020688"
    ],
    [
      "21435739948266173578080/67081",
      "-3137468248676342929871311536556080/17373979"
    ],
    [
      "243859843230968400",
      "-120362332081758768476537280"
    ],
    [
      "104222286079490939040/5041",
      "-997050253259905842053863275120/357911"
    ],
    [
      "2739289250202526800/169",
      "-4082763666617324166773111760/2197"
    ],
    [
      "143889931307632230060/37249",
      "494799577777326710719500807360/7189057"
    ],
    [
      "4294930541891040",
      "834638007028753640880"
    ],
    [
      "107349527602354836/25",
      "-306438416685685033765056/125"
    ],
    [
      "6556285940498177654880/1560001",
      "-48678867191471538240064329846480/1948441249"
    ],
    [
      "104506446187837900/9",
      "27543714424019930053480540/27"
    ],
    [
      "12320874007946940",
      "1141124473343389305468480"
    ],
    [
      "13284156751610400",
      "1310481222233810387940720"
    ],
    [
      "103260000815504640",
      "33089491507442908457627280"
    ],
    [
      "1109432993238331471530",
      "-36953162831912838804179582295510"
    ],
    [
      "5105061389726048340/1849",
      "14932639441279648341391124160/79507"
    ],
    [
      "12386226484516320",
      "1152433950992307113428080"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-1146, -2304, -654, 3054, 2880, -1830] with shift t=1295/6: 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 16 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 16:02:58",
  "updated_at": "2026-07-01 22:41:38"
}