{
  "id": 4010,
  "curve_key": "-15815364272792715246351888088719:-402509231861716350010793959459726138468683069321",
  "ainvs": [
    "1",
    "-1",
    "1",
    "329486755683181567632331001848",
    "465867166506616063474137421171883715144891979"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 219.2280944352601,
  "faltings_height": 16.329989136845914,
  "conductor": "12334433622321215895724716304610404854359954238330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "37",
    "43",
    "59",
    "67",
    "97",
    "137",
    "151",
    "157",
    "449",
    "631",
    "11551",
    "172351",
    "356533",
    "66670921"
  ],
  "discriminant": "-96047171028935992490827439854997921398381870379181168715638087486705253134164416716897600000",
  "regulator": "48314554385602796533121.138636269991148501595676012142499075497385233",
  "points": [
    [
      "-188628315440386890943/516961",
      "6406380700280005344189534038179/371694959"
    ],
    [
      "-42326073377526933219601/136212241",
      "29030805033529227510729559774501057/1589733064711"
    ],
    [
      "406869418669332689/961",
      "777572211194692969798802543/29791"
    ],
    [
      "11063220912160885303/15129",
      "61657378202238319942591964027/1860867"
    ],
    [
      "-5648013310341024527028510511842707/9582699073903941049",
      "242664361237581238949477851387710687565455148149877/29664140898554166018339994157"
    ],
    [
      "497442497498485852796194312207/3287018537540676",
      "4294068418055031077128910510057780093533978181/188453075766032782827576"
    ],
    [
      "-42784429875828653175156127/81588495769",
      "284360157140235711998779860245827325953/23304693165969853"
    ],
    [
      "310784355239063069573/1054729",
      "26278341152227399078516362164723/1083206683"
    ],
    [
      "489707948007750809522686213/508550118129",
      "14847235079877344768756673061602090982543/362660820090979383"
    ],
    [
      "621801173476972287817891487/14023519550401",
      "1151227185908140459161179617381345845952969/52515261988822114399"
    ],
    [
      "908172042911543833368498065453/369517154763241",
      "901888043680029518350425534800345484173563397/7103165078580317228789"
    ],
    [
      "11510368974701803752079736926927/5146575803850321",
      "41096863252812961492128609602662354182633209089/369213490254356838574119"
    ],
    [
      "7453009332098457113231879119389721/45875148684413409",
      "643428407649376215964043791771941464645470390208111/9825761702073337291413423"
    ],
    [
      "436766820470065275597154657591/11848534308900",
      "288688260266715264307996780632269357828013179/40784669342066313000"
    ],
    [
      "-49438395590173085781600097777/94218025320409",
      "11144717712154436770323649635922617568883683/914536401921006038173"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3645 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 15: 15 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 04:45:05",
  "updated_at": "2026-10-05 04:45:05"
}