{
  "id": 3342,
  "curve_key": "-534808463024:-31457547379964224",
  "ainvs": [
    "0",
    "1",
    "0",
    "11141842980",
    "36412912304100"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    6
  ],
  "naive_height": 81.01552352010359,
  "faltings_height": 4.820037990404755,
  "conductor": "39777459540",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "41",
    "137",
    "1297"
  ],
  "discriminant": "-89094643026019812274042404000000",
  "regulator": "1578.938956291323522017631558179115132242474747",
  "points": [
    [
      "-565360/289",
      "18778366950/4913"
    ],
    [
      "615240/1369",
      "325995405450/50653"
    ],
    [
      "5836049/256",
      "71211824775/4096"
    ],
    [
      "30960",
      "20274150"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#822 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 4 carries over. Torsion ℤ/6ℤ.",
  "created_at": "2026-09-26 21:03:50",
  "updated_at": "2026-09-26 21:03:50"
}