{
  "id": 5717,
  "curve_key": "0:27045663823542600",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-31302851647619"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 75.67260617016281,
  "faltings_height": 4.363706423305196,
  "conductor": "16932128047594465965509583675",
  "bad_primes": [
    "3",
    "5",
    "5008456263619"
  ],
  "discriminant": "-423303201189861649137739591875",
  "regulator": "22388301032170.66403919915278481350962471821292648679306284",
  "points": [
    [
      "35646997648001/693690244",
      "186675640193847449715/18270413646472"
    ],
    [
      "38268494849369/476636224",
      "229464118081208859869/10405922042368"
    ],
    [
      "3148825039492969/33969438864",
      "173187466998898464360341/6260839338146112"
    ],
    [
      "53045175644441/1047946384",
      "-336501517671585417885/33924120342848"
    ],
    [
      "69349215973721/1900262464",
      "-344567725232331344163/82836241330688"
    ],
    [
      "74483869361921/2129084164",
      "-333342186036111349125/98240201495288"
    ],
    [
      "484823255599961/12089442304",
      "7658299924696040426787/1329258360209408"
    ],
    [
      "3298819331703449/45705308944",
      "181410388596425960001507/9771246588519872"
    ],
    [
      "7564968854180561/79863890404",
      "645746335607971430205037/22569695155951208"
    ],
    [
      "58668883543112081/313915919524",
      "14176465948573309389524587/175881439222745768"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed using the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(13/4,-10/4,4/4) and specialization t=-1151/1178. The model is the rational 3-isogenous partner of the resulting Mordell curve. A three-stage Mestre–Nagao sieve selected the specialization. Ten rational points were reconstructed through the 3-isogeny, transformed onto the minimal Weierstrass model, and checked by exact rational arithmetic. PARI/GP 2.17.4 returned matching computational rank bounds [10,10] for both isogenous curves.",
  "created_at": "2026-10-24 15:54:30",
  "updated_at": "2026-10-24 15:54:30"
}