{
  "id": 3951,
  "curve_key": "5785462864654738839025:-439986986574478412665892988667625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-120530476346973725813",
    "509244197373943797663174128906"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "naive_height": 150.32890596448846,
  "faltings_height": 10.236962957316342,
  "conductor": "7107840925923552917025",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "19",
    "101",
    "239",
    "251",
    "311",
    "5519",
    "6229"
  ],
  "discriminant": "34744205120513052145261024329829466913014705809192578515625",
  "regulator": "24141627434.1507353065433175808196185804987206333631944",
  "points": [
    [
      "329367683411641/81",
      "-5977505773271651142745/729"
    ],
    [
      "994867752141/25",
      "-957966032517812851/125"
    ],
    [
      "556295686938050661/86638864",
      "-5734043841721732953519631/806434546112"
    ],
    [
      "12217539831021/1849",
      "-2886518137421240501/79507"
    ],
    [
      "195172207030341/29584",
      "177058867369767283849/5088448"
    ],
    [
      "387061648769655531/60310756",
      "-3001397447438889490253965/468373331096"
    ],
    [
      "4505398569814628716634125/685680462621001",
      "-555970402445902756864426481877241063/17954886439642684306501"
    ],
    [
      "4449715924110496165161/693487552081",
      "3508412279136878420122403496037/577508000383421479"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3669 (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 04:32:58",
  "updated_at": "2026-10-05 04:32:58"
}