{
  "id": 2626,
  "curve_key": "33910307590329:-197445732074518341933",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-706464741465",
    "228525329480211225"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 93.46422042843072,
  "faltings_height": 5.488652890395075,
  "conductor": "109819710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "53"
  ],
  "discriminant": "5179079606124995160871525788644100",
  "regulator": "26.0840665933376014431768592564593253814323",
  "points": [
    [
      "-868770",
      "432367425"
    ],
    [
      "221836",
      "287504795"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-30, q=23; A=(3q-p)(p+q)^3=-33957, B=-(p+3q)(p-q)^3=5806203. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 20:13:34",
  "updated_at": "2026-09-26 20:13:34"
}