{
  "id": 3961,
  "curve_key": "104403942071750928965812353:285965500608914539602884868185622571935",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-2175082126494811020121091",
    "-330978588667181391045789339126477334"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 179.7309289977022,
  "faltings_height": 13.04130102308199,
  "conductor": "2401768163536149420691858179",
  "bad_primes": [
    "3",
    "7",
    "11",
    "13",
    "23",
    "43",
    "47",
    "149",
    "991",
    "1153",
    "27031",
    "1246261"
  ],
  "discriminant": "611253367769755643367231849217796867438962402300183543227254655822772970409",
  "regulator": "455450380448.21172913142946134293863822829417355937898019",
  "points": [
    [
      "-10642720428605721/14884",
      "1682683133044167333383075/1815848"
    ],
    [
      "-139024865197974891/100489",
      "-5534663801616367781518675/31855013"
    ],
    [
      "21573413522060004589/1575025",
      "99613397327204672852585788827/1976656375"
    ],
    [
      "-4925766613921277968731/6318978064",
      "474106984472455408901908403924239/502308204263488"
    ],
    [
      "-1680276992110141151/1721344",
      "2096901619638400224799050175/2258403328"
    ],
    [
      "20438264785045981/289",
      "-2921267976654095336891635/4913"
    ],
    [
      "4232946352706235159909/1579188121",
      "-227114608877838799030210913625365/62755356740419"
    ],
    [
      "-4993903476966806499/7491169",
      "-18597726488538387968184815435/20503329553"
    ],
    [
      "-31695810175470706331/23464336",
      "-42882719888848147218063540535/113661243584"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3675 (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 04:34:56",
  "updated_at": "2026-10-05 04:34:56"
}