{
  "id": 6193,
  "curve_key": "856303584322194234270281864993041:-25079395262226190296576354202876619554343483111161",
  "ainvs": [
    "1",
    "0",
    "0",
    "-17839658006712379880630872187355",
    "29027077849798829875140020508779245542732275025"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 227.49226213367356,
  "faltings_height": 16.72579235795466,
  "conductor": "1188794000042104377137052333605459941590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "43",
    "53",
    "73",
    "107",
    "173",
    "659",
    "5323",
    "8599",
    "46831",
    "36841219"
  ],
  "discriminant": "-628745676826672242232861042641158360789873578285369299764569666353232169737004862008832000000",
  "regulator": "353246022778.944313472042639989994899664852088931643015261315",
  "points": [
    [
      "-4802148192467898",
      "62890460942565550753881"
    ],
    [
      "2299836332676690",
      "12774465094900746098745"
    ],
    [
      "2386676677881510",
      "6680631345728813167545"
    ],
    [
      "2627319692000160",
      "17102000496347926883145"
    ],
    [
      "3821811178138110",
      "129110676857779630536945"
    ],
    [
      "61892965167915726/25",
      "741999261265801017273261/125"
    ],
    [
      "1872552815328462190/729",
      "241961763583461953349448435/19683"
    ],
    [
      "4058743837415298750/1369",
      "2373863354831252581494750765/50653"
    ],
    [
      "5116941984840865920/3481",
      "15881682160280915181893956005/205379"
    ],
    [
      "108305308803576937230/44521",
      "47281853381422215219433659675/9393931"
    ],
    [
      "182803023014813659176/73441",
      "131883758588297684071217989047/19902511"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = 9095/7249 of the elliptic fibration of X648 given by:\ny^2 + (Lx+B)y = x^3,\nwhere\nL = 5098973881T^2 - 32101629380T + 51085836400,\nB = -2550648011199324171649113600T^5 - 231394683896910015292127210400T^4 + 1324630129545679262439545334000T^3 - 2330371426153230648960353010000T^2 + 1239686628515660725984584000000T.",
  "created_at": "2026-10-30 15:40:40",
  "updated_at": "2026-10-30 15:40:40"
}