{
  "id": 3990,
  "curve_key": "5768318119199013240497281:-13852543954129600711350227476250947265",
  "ainvs": [
    "1",
    "1",
    "1",
    "-120173294149979442510360",
    "16033036983896224913722494070540761"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "naive_height": 171.04326834823775,
  "faltings_height": 11.949843034662116,
  "conductor": "3070143408623089579456273867631802",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "19",
    "29",
    "59",
    "67",
    "97",
    "149",
    "151",
    "307",
    "349",
    "353",
    "2083",
    "2297",
    "3181"
  ],
  "discriminant": "22641140849527113851944380619876375069395668097762309633319687759872",
  "regulator": "208323921825272.96641126598785113420826111087044256466932750642",
  "points": [
    [
      "120756727232101/81",
      "-1293911795053632456091/729"
    ],
    [
      "2916291742506811/12321",
      "-39855221058234255971929/1367631"
    ],
    [
      "212566867441",
      "-9640683071029183"
    ],
    [
      "9887804979229/49",
      "-432038526700549/343"
    ],
    [
      "126912084027499/625",
      "29198104316744122643/15625"
    ],
    [
      "216196280501",
      "12538302278503101"
    ],
    [
      "7284632734456829/24649",
      "307890010445894550423153/3869893"
    ],
    [
      "26277699323489",
      "134692484491904967249"
    ],
    [
      "165053195711227861/106929",
      "-65492650714870972407845093/34965783"
    ],
    [
      "657697413460861/3249",
      "228026673956497509373/185193"
    ],
    [
      "5393212460509/25",
      "1520548192246297513/125"
    ],
    [
      "7397013230621171/34225",
      "79046985939160684432401/6331625"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3631 (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 04:40:45",
  "updated_at": "2026-10-05 04:40:45"
}