{
  "id": 4013,
  "curve_key": "34601944011569134296941746576:-6387059001305207853823817969339957011253440",
  "ainvs": [
    "0",
    "1",
    "0",
    "-720873833574356964519619720",
    "7392429399658565095092301567747888149044"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 197.14112212989014,
  "faltings_height": 14.282268844627849,
  "conductor": "66489049159927911945099447956450941788165109722672",
  "bad_primes": [
    "2",
    "3",
    "11",
    "43",
    "59",
    "67",
    "73",
    "347",
    "787",
    "907",
    "1097",
    "2113",
    "5659",
    "21517",
    "10645571",
    "39297109"
  ],
  "discriminant": "367011333797898087777115648950237465594860488974782568227096341989024359864635392",
  "regulator": "406718166969473811667.37377914519733243451449419744082762282716641093",
  "points": [
    [
      "25910323872167",
      "-78160848596915579034"
    ],
    [
      "1313886195259553/64",
      "-18070085119005361120623/512"
    ],
    [
      "85795684106519593094/4687225",
      "-184373985054995793338276516928/10147842125"
    ],
    [
      "13761849318615618471062/29149201",
      "1611859108744746702819592347408576/157376536199"
    ],
    [
      "30435877163985734",
      "5309804913811605767252832"
    ],
    [
      "6320942952688037452185911/306589227025",
      "-6105785330053918745340101754256740834/169759987949877625"
    ],
    [
      "11676302730208332041/640000",
      "-9062061196092489732558434661/512000000"
    ],
    [
      "1199288939303277413606/55696369",
      "-17896693327688765278809215114976/415662001847"
    ],
    [
      "23215362579448256006/1288225",
      "-23304850203779986267777147104/1462135375"
    ],
    [
      "183366094099292119/11025",
      "2208523931630298284995322/1157625"
    ],
    [
      "1136559083988407039/67081",
      "113161137419093907630442362/17373979"
    ],
    [
      "1222771186922767060234406/72551038609",
      "107598267515551129554893412315642336/19541839902449977"
    ],
    [
      "149612830618172639/361",
      "57751414440684555586586922/6859"
    ],
    [
      "72976163389128958214/3045025",
      "331022965852498148675048250912/5313568625"
    ],
    [
      "193473668311331855102726/10971934009",
      "14712012810578994999124390260016704/1149277171640723"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3648 (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 04:45:56",
  "updated_at": "2026-10-05 04:45:56"
}