{
  "id": 3686,
  "curve_key": "72884462827799658760207908574176:-622231951883554942410783830668807256755372836576",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1518426308912492890837664761962",
    "720175870235595998160629433644452843466866709"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 220.09928482855923,
  "faltings_height": 15.881632107284158,
  "conductor": "172186176309954886778696599644848520",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "29",
    "31",
    "41",
    "43",
    "89",
    "107",
    "269",
    "433",
    "443",
    "449",
    "4651",
    "6367"
  ],
  "discriminant": "131444724855103147535741008773370636476180862699402521916988229065221609234113191490000",
  "regulator": "428166317.2371747764046064406920563868413479815865966924092",
  "points": [
    [
      "-825110947090247",
      "37567324159599876037110"
    ],
    [
      "-321734683300562",
      "34284143407089487452255"
    ],
    [
      "251272242256153",
      "18828230090132452184910"
    ],
    [
      "710920229087173",
      "18915847531589385000"
    ],
    [
      "721473473611138",
      "464548931739172394595"
    ],
    [
      "936517883952658",
      "10932988333851045777645"
    ],
    [
      "-277273875475751207/256",
      "135489746744220032632980765/4096"
    ],
    [
      "6422721546455002/9",
      "2716260595248925494055/27"
    ],
    [
      "14462044121030497/4",
      "1649086239767378700884895/8"
    ],
    [
      "659801767248118585/961",
      "34009992844212199882633722/29791"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 886/615 of the Elkies-Klagsbrun Z/4 fibration E2: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = -8(80t+9), c = 2(t-2)(2t-1)(18t-1)(2t-81) (arXiv:2003.00077, eq. (6)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:33:00",
  "updated_at": "2026-09-29 19:33:00"
}