{
  "id": 4017,
  "curve_key": "5480954432795637699898808831444881:79208137489524044698335410956519187915765953062215",
  "ainvs": [
    "1",
    "0",
    "0",
    "-114186550683242452081225183988435",
    "-91676085057319505694174838136545992782383333599"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 233.05976196350022,
  "faltings_height": 17.48753089707841,
  "conductor": "2050943799731838770795008718676624626173063235165279006502",
  "bad_primes": [
    "2",
    "3",
    "11",
    "47",
    "137",
    "167",
    "179",
    "293",
    "307",
    "353",
    "433",
    "439",
    "1193",
    "1697",
    "2647",
    "4787",
    "5393",
    "10211",
    "20161",
    "26863",
    "34961"
  ],
  "discriminant": "91654319402820768998633513846140928169165800422073578783584478927601135172740270483687126071001472",
  "regulator": "1004280681999548490389979.229253961861947900108606471390095023195075731",
  "points": [
    [
      "-88187849110945654484/22801",
      "-1860809724191803949186280039059/3442951"
    ],
    [
      "12667215611016406",
      "-703177644289230010996007"
    ],
    [
      "26119613818766527541303668/1228572601",
      "114664380199031056378126469747732483369/43062698237651"
    ],
    [
      "763593796062471255647174902/7493152969",
      "20983294424884567755731540838576242385883/648629800455547"
    ],
    [
      "124048580120012893221121/4426816",
      "40290592049728136753898257559608827/9314020864"
    ],
    [
      "4186017578186409739646253826/15708862225",
      "270614492118712172227657339498660807431019/1968870246970375"
    ],
    [
      "23105024159530183634031778/215766721",
      "-110501985139847730091392571459809976739/3169397364769"
    ],
    [
      "43111103429384047795328269426/3878028271441",
      "863150390950262895617223325808178284681831/7636888612128889511"
    ],
    [
      "-365677591322770660565114/67256401",
      "-334796437975888563475099053677400679/551569744601"
    ],
    [
      "5853613340851598414035846/26224641",
      "14146076854748604835262973389707602073/134296386561"
    ],
    [
      "3121488941948439398367070161555964/90320238563028049",
      "165649028560432046532366255482145964376059795678753/27144235468363819348325593"
    ],
    [
      "2132079436748742664475190673648/119414867699521",
      "-2462554253249855541445513740545324048295683327/1304931163323600326431"
    ],
    [
      "-120868623567811994188833015862694/12231851024094601",
      "-362480436468765681618805584559222217279600655193/1352814577775656428923099"
    ],
    [
      "-35093227670839723986087298291662118496/3726388669816705368025",
      "-87642771361136775592801574094966336353507863314935191373/227474241756000402510073296596125"
    ],
    [
      "8347519659862572621548137562135776/690527246854455481",
      "-311413793840365921368271645810597162864650053541347/573814118218196137574636371"
    ],
    [
      "6064491994805139867726242662/112766341249",
      "-462712674903173033403502187113165207342681/37867726755802943"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3653 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 16: 16 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 04:46:39",
  "updated_at": "2026-10-05 04:46:39"
}