{
  "id": 3987,
  "curve_key": "86104931406086909242353059125782577483402516619025:-719046188416698991081297882660542882319496199085765835049622137219016517625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1793852737626810609215688731787137030904219096230",
    "832229384741549758195947071912886816794661793604782292906505570058265397"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "naive_height": 344.9389534465192,
  "faltings_height": 26.718768867819584,
  "conductor": "1097108044453769307704470853301745036152608455549132667550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "31",
    "43",
    "47",
    "71",
    "109",
    "139",
    "167",
    "181",
    "227",
    "271",
    "523",
    "947",
    "1061",
    "1063",
    "11953",
    "4943153",
    "588848633"
  ],
  "discriminant": "70231272483696067720627399053055454118099559294743153994968537650390513887501605443406693368836654448903659395193667227782384322099443507600000000",
  "regulator": "288443385334928656152.30947907030789717825272427704425729232812",
  "points": [
    [
      "3281863077864858598767454585313805569/3360149291041",
      "671659342332070829460883502635450506963216364318831845/6159392221077816911"
    ],
    [
      "-525258446587894515009782370314174151/1005276943225",
      "1285598605119671106038163531791472073956201666806445673/1007925847970397875"
    ],
    [
      "13009814654158865574890813666442975267/23788221118489",
      "-14089724016900461438956393746735066873392393262681536275/116022695260965414013"
    ],
    [
      "-81033233492919750136498140442776978715917511/270174766463323957921",
      "-5146950066588254995720030663710091045909149944215621318414864939995/4440860971810919715808572248719"
    ],
    [
      "3809320519976728034503574833937222766852051/6756350274754861225",
      "-135286858520406513859801845048081638288822382481462012602932229/17561767992942020888840192875"
    ],
    [
      "-6724212050408828785850191989544531276779/4418159201485225",
      "-56525967047627242621044122535763204240873272879485880780411/293671662230933769552875"
    ],
    [
      "247425017983165740382355120863215180473425207797/5244244217067708230569",
      "-123024632029499097808144795585922720578382239871778794960833786281854495/379773241935813462742219222208747"
    ],
    [
      "-740656292060759081184280332919365518755796425891/1188712876906001327802601",
      "-1693810097832531377652208410260699394054850015964330099881711111130864145/1296031182956615367555874333423167349"
    ],
    [
      "48497036059054204068501428708491880610869698282769/156215155443570618756120841",
      "-1078726621120931336323385639146661463254321436397114149036065236477672944345/1952471700992596398616714653848491244389"
    ],
    [
      "5380319778634861125029936894310759905553888679986110021/14952583561138132779331650087025",
      "-27930094887965596168251694592963449693888668995462881779121252602387398768068981809/57819503383385437166516141367950583244849327625"
    ],
    [
      "5252039869525281657957310900921884564023198481/5371894581238612380409",
      "-44801601035786113693176470534904933786959871159875927418060843313585/393723395776536257616118226888077"
    ],
    [
      "15161956867426857100882170821668777938025811806612851/8687173378237296169861124089",
      "-1406604335822926647376650186078539516961674695146303101673937755004245769744365/809688057782855652104075785048469907000563"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3706 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 12: 12 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 04:40:04",
  "updated_at": "2026-10-05 04:40:04"
}