{
  "id": 3998,
  "curve_key": "1321133208615491871861481:-1518491313130821826169318556477288565",
  "ainvs": [
    "1",
    "0",
    "1",
    "-27523608512822747330448",
    "1757513093899120516616198285497102"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 166.62159627461338,
  "faltings_height": 11.52899827345843,
  "conductor": "551664926630833203374698683114972985506",
  "bad_primes": [
    "2",
    "3",
    "11",
    "23",
    "47",
    "53",
    "59",
    "89",
    "157",
    "251",
    "317",
    "521",
    "7607",
    "9533",
    "55997",
    "95569"
  ],
  "discriminant": "46716873234351036450295482854502951294135814155220556820726813072",
  "regulator": "57045032385808008.18910216333016948425548331669052612309016721625",
  "points": [
    [
      "140887294038794/49",
      "-1669551509974540502871/343"
    ],
    [
      "459657693664721/625",
      "-9623205723589619754681/15625"
    ],
    [
      "201486730027061/1681",
      "-925989536352909602637/68921"
    ],
    [
      "485630208248474/4489",
      "-2040941007148613559291/300763"
    ],
    [
      "140214865743002/1369",
      "-182083315440928932162/50653"
    ],
    [
      "17247910730249/169",
      "-7460335409400588645/2197"
    ],
    [
      "93473509483493/961",
      "-23165144498961170475/29791"
    ],
    [
      "7612555210427812682/64368529",
      "-6461841259800052175078788518/516428708167"
    ],
    [
      "1468989065032661/14161",
      "-7275208548279349626003/1685159"
    ],
    [
      "2119667027238961/9216",
      "77098427401117236495865/884736"
    ],
    [
      "1517242841047361/3136",
      "56002163865331757544603/175616"
    ],
    [
      "156994524195506/961",
      "1199456461544758819833/29791"
    ],
    [
      "7975796181397927109/82319329",
      "-423365130488066672845977345/746883272017"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3638 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 13: 13 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 04:42:48",
  "updated_at": "2026-10-05 04:42:48"
}