{
  "id": 4019,
  "curve_key": "268578891633472573536247397643879915575041:134417028810268475713714921180234285701202327779824407690960255",
  "ainvs": [
    "1",
    "1",
    "1",
    "-5595393575697345282005154117580831574480",
    "-155575264826699624670982943133663576392041878775640633168719"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "naive_height": 286.1818899634421,
  "faltings_height": 21.769797085977057,
  "conductor": "199500119263603519815431870142834901369753749343131572760786463422",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "19",
    "29",
    "31",
    "37",
    "43",
    "47",
    "59",
    "61",
    "83",
    "163",
    "193",
    "263",
    "653",
    "701",
    "947",
    "1693",
    "2311",
    "4637",
    "10457",
    "56599",
    "57329",
    "7057319"
  ],
  "discriminant": "755728547883892635943672209275166861463045058530861411150682843908683617224785189292255508270661903285874141897894751232",
  "regulator": "591399625560959953580669486.540606602694630287462101833071314527965420448",
  "points": [
    [
      "-397120289686607819252477535659/8015441841",
      "4002220565116303446226241075993945381044189/717614492582889"
    ],
    [
      "-95178059711366656572513553830999/2236810386409",
      "247466280794418917560725677646144232326373593817/3345366903482141173"
    ],
    [
      "-4555964533352491648726626171133959/105366940225600",
      "80385402140113749470594249439961748573744202662119/1081574782705347904000"
    ],
    [
      "133372353561603835232770138574419/1486119474225",
      "-462223167098079121066239442966203565483501398983/1811676236846099625"
    ],
    [
      "11509457247428618222555054221/131767441",
      "224823911822689808441910936807205844684843/1512558455239"
    ],
    [
      "-1245750142958115454748871838941834219/25681199967095401",
      "-169942300414667638145164194064063009655348114810840887/4115503437305721231828149"
    ],
    [
      "72402795866076380175086026027581/641205367009",
      "414692339578658540444704638763223679185483670893/513447121248557777"
    ],
    [
      "-4551183752610281082310101186996131/107046730702921",
      "-81884020395779748064697142064366739511048859469561/1107541764694128956219"
    ],
    [
      "7283953096127815283420950001581/53160219225",
      "15745046179407870864853355794741305081132209201/12256885945612125"
    ],
    [
      "601902580777803065717822777611899/566861421604",
      "14729248584996985894864951505473650393453043873423/426791098048494808"
    ],
    [
      "1832038050407961406793023534278847954501/7830389869187657641",
      "73795339359578764007869656645438805799020590918979987078079/21911649822037806608752648939"
    ],
    [
      "1211812840339376994076684226974676399876161/552343044131733017241",
      "1333206894152538729677153264155990173982092055908690491720907523/12981154943786685157078036921539"
    ],
    [
      "-1618375281168173851599557034594675669/41755820524608100",
      "-472725136797358005608551808130371442784061364861054751/8532484997525883459521000"
    ],
    [
      "-3030271550347372806453590783703540107120711/61152791712040224731089",
      "-62055995304688409170930093394824702726239221591352420063519911/15122529207764968696651707861670937"
    ],
    [
      "205637088171306361594036578304161722491/1789527786727228900",
      "-2029622328896132006420457465332188854729262817177263380179/2393909175738358990840337000"
    ],
    [
      "9925267153564510158810034195307509541832114789/51531907874307708644948281",
      "899433297734042989953606486113995584964025230849923634037224742842721/369925553739878968721619845255114936429"
    ],
    [
      "16544405814662945651335577432508543672008941/1466286284766650248521",
      "-67292582234490815895378250576530028990103111793014495403796152551/56147207128679767695332255040069"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3472 (source contributor: Steps Unbounded). Source equation and witness provenance are credited to that entry. Exact rank 17: 17 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:47:06",
  "updated_at": "2026-10-05 04:47:06"
}