{
  "id": 3713,
  "curve_key": "81487299596375460507201:-23261348556340145767110773644200801",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1697652074924488760567",
    "26922857125818100249183406500559"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 158.26420238341566,
  "faltings_height": 10.531522543796203,
  "conductor": "85197380776083810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "337",
    "373",
    "3253",
    "4813"
  ],
  "discriminant": "4855332772164102056902166957704065685416609811392000000",
  "regulator": "1903714.0615210610144222991754911724356348930535098",
  "points": [
    [
      "32565940550403/1369",
      "1916690683463398/50653"
    ],
    [
      "148517173268707/6241",
      "1139866002758464834/493039"
    ],
    [
      "1247479754125947/52441",
      "-30700259370662426/12008989"
    ],
    [
      "1451298031714203/61009",
      "-125292958643562182/15069223"
    ],
    [
      "93034233729817587/3876961",
      "425463246363818304640894/7633736209"
    ],
    [
      "256740174301684083/10804369",
      "243275883642332641669778/35513960903"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 1068702/4849 of the universal curve with a 6-torsion point, y^2 + txy + (t+2)y = x^3 (as searched in arXiv:2003.00077, Sec. 13), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:48:13",
  "updated_at": "2026-09-30 01:48:13"
}