{
  "id": 3960,
  "curve_key": "139536532646095487802176473:-1648278450126315141541722879592363599005",
  "ainvs": [
    "1",
    "1",
    "0",
    "-2907011096793655995878676",
    "1907729687644986825864441161381767680"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 180.60110604480275,
  "faltings_height": 12.646634761905965,
  "conductor": "3682590235087728259825836306",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "37",
    "53",
    "71",
    "131",
    "199",
    "311",
    "769",
    "1721",
    "3449"
  ],
  "discriminant": "9483634788704864364684565948484900056238531055313502227951058119048464",
  "regulator": "1408409147350.5047319051739768801946006976775348703743630",
  "points": [
    [
      "1282891082724",
      "-538280721199788192"
    ],
    [
      "9274594093841388420/9406489",
      "38646989915929023227631840/28849701763"
    ],
    [
      "65709108225797076945/66455104",
      "3882301438885123083248314485/541742007808"
    ],
    [
      "48767500046833077156601/38865362449",
      "-3719749216575499113144234750665714/7662034149283207"
    ],
    [
      "3491725482156010705/3538161",
      "23676102979768437298957405/6655280841"
    ],
    [
      "18582785464269145/18769",
      "-24440907757968192049390/2571353"
    ],
    [
      "21733629214911145/12769",
      "1984029677932876325715650/1442897"
    ],
    [
      "541789291885967277976305/534289364401",
      "19981490413977838986465666439353510/390539345198275351"
    ],
    [
      "106828547283928418840505/65249082721",
      "20663080309929020237344192505669595/16667160441169519"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3677 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 9: 9 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 04:34:46",
  "updated_at": "2026-10-05 04:34:46"
}