{
  "id": 3959,
  "curve_key": "3538114636721014424307368961:-209508276899687887515839125254331283998209",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-73710721598354467173070187",
    "242486431596879408601509687290787809211"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 190.30017452283718,
  "faltings_height": 13.68982847161782,
  "conductor": "2108987770780492075994930190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "31",
    "37",
    "67",
    "101",
    "137",
    "181",
    "191",
    "199",
    "331",
    "929",
    "947"
  ],
  "discriminant": "229921179523637184549007573553619706800136331315966054011987378837002332160000",
  "regulator": "4885363903229.2747136166046105111272682457864311694270507",
  "points": [
    [
      "90418383666522621131/15594601",
      "194970734236873131242288058666/61583079349"
    ],
    [
      "175142157432123014219/84364225",
      "7686948691091154773019926825802/774885406625"
    ],
    [
      "85095988299911205/21904",
      "-12454067624049618816779881/3241792"
    ],
    [
      "93700961242952338368304451/34042685521321",
      "1544353637683157006074579466674849092654/198625827412240241131"
    ],
    [
      "47717120459388395/2401",
      "-9577487157648958949295222/117649"
    ],
    [
      "2010145216694137281460395/357842043601",
      "510259450193681715704728808983869478/214060752640074599"
    ],
    [
      "24999274130820227682371/6969745225",
      "2865048099344333326031386458900114/581869180109125"
    ],
    [
      "627074160325964688024395/26331877441",
      "467929098575539953314698617788608182/4272900084228511"
    ],
    [
      "-974406782620689839735867461/2988474000961969",
      "-2666926348912612301755247254645622198596998/163370719936725898718953"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3674 (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 04:34:35",
  "updated_at": "2026-10-05 04:34:35"
}