{
  "id": 3944,
  "curve_key": "5519336584372689393:-12966215535286936522078234185",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-114986178841097696",
    "15007193935328647166383491"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "naive_height": 129.46436802890608,
  "faltings_height": 8.45595128179136,
  "conductor": "1354000263461127126",
  "bad_primes": [
    "2",
    "3",
    "13",
    "19",
    "31",
    "37",
    "59",
    "109",
    "163",
    "241",
    "1051"
  ],
  "discriminant": "7654144671633140700386977387894433429066165362944",
  "regulator": "128047967.5691548883955931150683056052836895166917247",
  "points": [
    [
      "24930430451993/2809",
      "-124389699933139204539/148877"
    ],
    [
      "108276380530713/38809",
      "-1118730119383494649163/7645373"
    ],
    [
      "873793217",
      "-24118623325851"
    ],
    [
      "3213661092329/15625",
      "-470208470526303267/1953125"
    ],
    [
      "64296090680657/1681",
      "-515538320422833376131/68921"
    ],
    [
      "209386365969/625",
      "-58645785666770847/15625"
    ],
    [
      "96356131460753/485809",
      "19385016699743523777/338608873"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3663 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 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 04:31:31",
  "updated_at": "2026-10-05 04:31:31"
}