{
  "id": 4670,
  "curve_key": "1330962884666272737290998161:-48281983015704681355748880470878573670841",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-27728393430547348693562462",
    "55881924786702165148992915159949517549"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 187.3671004936915,
  "faltings_height": 13.454881768854891,
  "conductor": "267850366109224468929137248470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "31",
    "43",
    "59",
    "113",
    "131",
    "2239",
    "32401",
    "1213873"
  ],
  "discriminant": "15393840473670775536345619115358466634977146502004418756018583783104000000000",
  "regulator": "200926415615.5679519571584663822134835445739622196448177793",
  "points": [
    [
      "-6044372458743",
      "1629392165978923171"
    ],
    [
      "19243712248857",
      "81539092004797715971"
    ],
    [
      "-6032726129661687/2209",
      "1095021550276840165366733/103823"
    ],
    [
      "-29199304563503/121",
      "10527460730005843528601/1331"
    ],
    [
      "158974705478313/49",
      "91288649947688335813/343"
    ],
    [
      "44439094929380433/1369",
      "9251690289441687577264663/50653"
    ],
    [
      "303030999696733909/180625",
      "288096770995119078767554727/76765625"
    ],
    [
      "54770745510572501121/16933225",
      "12809154872133130877865568961/69680220875"
    ],
    [
      "283338413439504673137/87815641",
      "59073586534654230883187360681/822920371811"
    ],
    [
      "4017287537690907281793/468419449",
      "214791503402314532898750271549897/10138002134707"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Rank exactly 10 by PARI/GP 2.17.4 ellrank. Constructed by specializing a rank-5 elliptic K3 deformation with rational 3-torsion at w=8/3, t=121/41. Found by precomputed Mestre-Nagao sieving of 27,892,344 rational parameter pairs.",
  "created_at": "2026-10-20 19:44:01",
  "updated_at": "2026-10-20 19:44:01"
}