{
  "id": 3608,
  "curve_key": "7967431953469404375521601:-21902906430667722896791096153604242401",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-165988165697279257823367",
    "25350586146647657801599199621868159"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 172.01221337585346,
  "faltings_height": 12.242746905465378,
  "conductor": "549866032239950391699315764116011233874518242613990",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "29",
    "73",
    "89",
    "586543",
    "2651485605367",
    "158625189154131660367301"
  ],
  "discriminant": "15066577936954046198817155090494224960826559686786591648004311552000000",
  "regulator": "13743313880425379877964.9863611525593534537779114009576976364904783427267",
  "points": [
    [
      "-427204525407338756549/925802329",
      "1711169811438529288062172457194/28169387464483"
    ],
    [
      "-50305429171462094549/1471106025",
      "9932383491820156897377264805786/56424271588875"
    ],
    [
      "-10608353191848937937/354681889",
      "1162511038573230723163942188242/6679724015537"
    ],
    [
      "-202601865058275037/1776889",
      "489985859314892268957586742/2368593037"
    ],
    [
      "-75655878214689317/165649",
      "5174267783151998306124138/67419143"
    ],
    [
      "-20308271840434289/45369",
      "964500153210098341438246/9663597"
    ],
    [
      "8005580883603/289",
      "708116619595559370078/4913"
    ],
    [
      "67190974728046051/330625",
      "629128409544618073562226/190109375"
    ],
    [
      "77017645148428917/724201",
      "58143751485889088626940766/616295051"
    ],
    [
      "1096982426593737051/5822569",
      "388721555462329376047021094/14049858997"
    ],
    [
      "7388271113818239047/7540516",
      "18559054581501057183195958951/20706256936"
    ],
    [
      "2884262485475425083/1841449",
      "4746466917855211093951072038/2498846293"
    ],
    [
      "10108773481877691833/67354849",
      "34161904948160139535959657238/552781245743"
    ],
    [
      "11136348878435309643/27321529",
      "22765770469104127585382959178/142809632083"
    ],
    [
      "61743867177087034437/622801936",
      "1544057393180285422980343488531/15542645114816"
    ],
    [
      "23502680366205605227/86694721",
      "13400220258348762071314741626/807214547231"
    ],
    [
      "1339931415992813303427/6600100081",
      "2380004642221798065685453466286/536198730680521"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 3 of the rank-17 fibration of X1092, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #724 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:18:26",
  "updated_at": "2026-09-29 19:18:26"
}