{
  "id": 3939,
  "curve_key": "9086423308347152986587729:-27412597607222584852917633781956650457",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-189300485590565687220578",
    "31727543526925316849311569410180897"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 172.4081320444126,
  "faltings_height": 12.134010278440709,
  "conductor": "1693477477526556829770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "37",
    "43",
    "61",
    "67",
    "97",
    "103",
    "271",
    "4327"
  ],
  "discriminant": "-721837656470908215502510470839565632841071067029282872684969243485120",
  "regulator": "254625068.3629504009668567856281370530687809766246993",
  "points": [
    [
      "-62735041473",
      "208222056986129215"
    ],
    [
      "1880606690186989/784",
      "80296790176689161547373/21952"
    ],
    [
      "2527315176420147945/31663129",
      "23316463311692726924379089669/178168426883"
    ],
    [
      "6843118422691238143/27857284",
      "1033083481092048085415064805/147030744952"
    ],
    [
      "3601224276034917/14641",
      "12119809055254839510415/1771561"
    ],
    [
      "118642613265825564027/456292321",
      "90183787242408876581775779965/9746860268881"
    ],
    [
      "152214093721596524815/5595488809",
      "68262561723885606296843144968581/418559349379627"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3719 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 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 04:30:24",
  "updated_at": "2026-10-05 04:30:24"
}