{
  "id": 3956,
  "curve_key": "91759201203720987153:-731385631006085896486136397945",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1911650025077520566",
    "846511147475697108683889861"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "naive_height": 137.89709832419513,
  "faltings_height": 9.491316217039648,
  "conductor": "830429816548607909946",
  "bad_primes": [
    "2",
    "3",
    "13",
    "23",
    "29",
    "41",
    "53",
    "101",
    "883",
    "1613",
    "17021"
  ],
  "discriminant": "137537433657905572676935732566488528096478137409861648384",
  "regulator": "1385191688.54704763857461304655073465784002336102223512",
  "points": [
    [
      "-178841415",
      "34390105909307"
    ],
    [
      "226531531589/25",
      "-106618502581102173/125"
    ],
    [
      "490368290337/169",
      "-308591888730042009/2197"
    ],
    [
      "67777910265/64",
      "-1600262076959321/512"
    ],
    [
      "-420278159639/1089",
      "1404216684167139275/35937"
    ],
    [
      "84786321086665/74529",
      "-244237226109895342661/20346417"
    ],
    [
      "12403219317177/37249",
      "-112960317620961876789/7189057"
    ],
    [
      "217259175179085/58081",
      "-3003319986841042101073/13997521"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3666 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 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 04:33:56",
  "updated_at": "2026-10-05 04:33:56"
}