{
  "id": 1113,
  "curve_key": "557713:-400025305",
  "ainvs": [
    "1",
    "0",
    "0",
    "-11619",
    "462024"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 39.694799316387844,
  "faltings_height": 1.2360395161314126,
  "conductor": "14763",
  "bad_primes": [
    "3",
    "7",
    "19",
    "37"
  ],
  "discriminant": "7785255102849",
  "regulator": "3.28026810609458732173296481990354897968927",
  "points": [
    [
      "-117",
      "531"
    ],
    [
      "-75",
      "993"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 14763h2: the smallest-conductor elliptic curve over Q with rank 2 and torsion subgroup Z/2Z x Z/4Z, per Cremona's tables (PARI elldata scan of every curve with this torsion up to conductor 14763; ellrank proves rank exactly 2 and no smaller-conductor case was left inconclusive). Generators (-117, 531) and (-75, 993).",
  "created_at": "2026-09-23 20:39:54",
  "updated_at": "2026-09-23 20:39:54"
}