{
  "id": 3734,
  "curve_key": "140103387025:7028693958622375",
  "ainvs": [
    "1",
    "1",
    "1",
    "-2918820563",
    "-8136278627344"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "naive_height": 76.99693939729336,
  "faltings_height": 4.483551658995193,
  "conductor": "877303616925",
  "bad_primes": [
    "3",
    "5",
    "19",
    "31",
    "79",
    "101",
    "131"
  ],
  "discriminant": "1562894160150133461771453515625",
  "regulator": "1603.5006112337355748485848846933513753678545918178",
  "points": [
    [
      "-62925/4",
      "46633421/8"
    ],
    [
      "-5284",
      "2674583"
    ],
    [
      "-4600",
      "2281112"
    ],
    [
      "353550",
      "207556162"
    ],
    [
      "-221786/9",
      "189000110/27"
    ],
    [
      "17964425/256",
      "47023143677/4096"
    ]
  ],
  "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 2096 + 2449 = 4545 and twist d = -95. Candidates were screened with Mestre–Nagao sums and then checked with PARI/GP 2.17.4. PARI/GP ellrank at effort 2, supplied with the six listed points, returns matching lower and upper bounds [6,6]. This improves curve #3725 (conductor 3975391189200), submitted earlier on 2026-09-30, by a factor of about 4.53.",
  "created_at": "2026-09-30 20:57:49",
  "updated_at": "2026-09-30 20:57:49"
}