{
  "id": 3656,
  "curve_key": "62596842998848:-495253791164926660096",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1304100895809",
    "573209971740588735"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4
  ],
  "naive_height": 95.30320788430377,
  "faltings_height": 5.527113659526265,
  "conductor": "50691232704",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "71",
    "73",
    "383"
  ],
  "discriminant": "547233200555888196890935054958592",
  "regulator": "449.806296513330274238482436861770554682269689399",
  "points": [
    [
      "569327",
      "123645648"
    ],
    [
      "634434",
      "34759683"
    ],
    [
      "2645301/4",
      "20975601/8"
    ],
    [
      "31829241/64",
      "111762495789/512"
    ],
    [
      "370004223/529",
      "693383647344/12167"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -17/16 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:27:58",
  "updated_at": "2026-09-29 19:27:58"
}