{
  "id": 3661,
  "curve_key": "10419647936084161:-1274570424557278860667841",
  "ainvs": [
    "1",
    "1",
    "1",
    "-217075998668420",
    "1475197160196665902820"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 111.00930286356137,
  "faltings_height": 7.247891273522263,
  "conductor": "526770622069324545",
  "bad_primes": [
    "3",
    "5",
    "11",
    "31",
    "109",
    "421",
    "653",
    "1709",
    "2011"
  ],
  "discriminant": "-285462009710170752549372769612564542464571375",
  "regulator": "96452497.77820866435814646489370282074492545991450175",
  "points": [
    [
      "-2992144239112/2193361",
      "136618752273576291323/3248367641"
    ],
    [
      "-906085517/81",
      "36481078215422/729"
    ],
    [
      "21663521376110/32041",
      "100805243520592187555/5735339"
    ],
    [
      "6382410131798320/20820969",
      "509299870343990692776265/95006081547"
    ],
    [
      "10978932388407232/546297129",
      "923244303477017871921671/12768602796117"
    ],
    [
      "25279721799429232/3341649249",
      "3149518437906086342220524/193170718136943"
    ],
    [
      "13456551732858453332/520898523289",
      "43037005371582297864541349876/375949653908939837"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -25/198 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 19:28:48",
  "updated_at": "2026-09-29 19:28:48"
}