{
  "id": 3725,
  "curve_key": "2241352800400:-3346996096249208000",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-46694850008",
    "3873853639312512"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "naive_height": 85.31430218476176,
  "faltings_height": 4.918382352390649,
  "conductor": "3975391189200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "29",
    "71",
    "109",
    "509"
  ],
  "discriminant": "33227353062822801888435600000000",
  "regulator": "1868.9035775798831209969834779375000616109096155105",
  "points": [
    [
      "45772",
      "42806900"
    ],
    [
      "77552",
      "26814000"
    ],
    [
      "132302",
      "3435750"
    ],
    [
      "-664532/9",
      "2245890500/27"
    ],
    [
      "611157/4",
      "139978563/8"
    ],
    [
      "3417494/25",
      "839871378/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found 2026-09-30 in a direct search of the full rational 2-torsion family y^2 = x(x+da)(x+db), using the primitive smooth additive relation 71 + 2545 = 2616 and twist d = 145. Candidates were screened by a deep Mestre–Nagao sieve and then checked with PARI/GP 2.17.4. The submitted six points are independent; PARI/GP ellrank with these points returned matching lower and upper bounds [6,6]. Conductor 3975391189200. ",
  "created_at": "2026-09-30 20:06:30",
  "updated_at": "2026-09-30 20:06:30"
}