{
  "id": 3999,
  "curve_key": "1051575766958561664510481:-1078296837600500549203082497768320121",
  "ainvs": [
    "1",
    "0",
    "0",
    "-21907828478303368010635",
    "1248028747220975909204449832490225"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 165.93699600447812,
  "faltings_height": 11.503580718188735,
  "conductor": "8517544174435024143004460515381044430",
  "bad_primes": [
    "2",
    "5",
    "31",
    "151",
    "193",
    "199",
    "241",
    "311",
    "409",
    "1031",
    "1721",
    "2333",
    "2437",
    "2711",
    "5651"
  ],
  "discriminant": "69794403730586320988601187786447125765118962818761998220526720000",
  "regulator": "6834075770812159613.654171211417756425642445726615359654427006552",
  "points": [
    [
      "12921074909308473707143817902/20095038597001",
      "1468750225749362607427326272359176790434309/90081014175667635749"
    ],
    [
      "78400493914408568492590/43734938641",
      "-21879645145112636398300520154589815/9146243983053689"
    ],
    [
      "79072786865973460/24649",
      "-22211922560113929001340905/3869893"
    ],
    [
      "584855021779465531270/5773112361",
      "-3626082616125801748432448686235/438646850301141"
    ],
    [
      "37376842090344422005/401120784",
      "31829499291409293464076178705/8033647061952"
    ],
    [
      "37505176948053655024270/421732049281",
      "-480258634120904204700171138386415/273876588391524929"
    ],
    [
      "75898078623859500190/13111641",
      "661006090242751209890417208445/47477252061"
    ],
    [
      "11892053159319008500026708670/137738714250198889",
      "-18826577591764503419657496444702690718805/51119198630112968756117963"
    ],
    [
      "141743432239032243215620/1580066598049",
      "4281442736440154084090564138816015/1986154774213779343"
    ],
    [
      "11265924127192495004104330/130849874515369",
      "304718550238512990083074514203793455/1496786873135948922347"
    ],
    [
      "215999690152284618775/2492605476",
      "68915183167755027836296547015/124445820994776"
    ],
    [
      "1011717182596484773080730210/11655341519448649",
      "-799124833574161755780053068060253579565/1258309586492914837315643"
    ],
    [
      "334599681395808207968281510/3812327833890601",
      "270287827483557393790015350467566964315/235388564204460796564651"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3635 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 13: 13 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 04:42:58",
  "updated_at": "2026-10-05 04:42:58"
}