{
  "id": 1118,
  "curve_key": "11207483582641:-37538252159773363561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-233489241305",
    "43447031653412025"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    12
  ],
  "naive_height": 90.14378428911584,
  "faltings_height": 5.259834882740535,
  "conductor": "36817770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "31",
    "59",
    "61"
  ],
  "discriminant": "-795295855006123967199000000000000",
  "regulator": "14.8260610854632474985206556795595187448168",
  "points": [
    [
      "282510",
      "5485995"
    ],
    [
      "135354715/484",
      "47972566885/10648"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rank exactly 2, torsion Z/12Z. Found by a small-parameter search of the universal family y^2=x^3+2(3t^8+24t^6+6t^4-1)x^2+(t^2-1)^6(1+3t^2)^2*x at t=1/11, followed by passage to the global minimal model. Family: Halbeisen, Hungerbuehler, Shamsi Zargar and Voznyy, Theorem 4.1, https://arxiv.org/abs/2106.06861 . PARI/GP ellrank gives lower and upper bounds [2,2]; two independent rational points are supplied. Conductor 36817770. This fills the rank-2 gap on the Z/12Z board.",
  "created_at": "2026-09-23 20:56:03",
  "updated_at": "2026-09-23 20:56:03"
}