{
  "id": 430,
  "curve_key": "5081008373394232174337128526351232241:-11236201971629578109957395024293521667519729886732725961",
  "ainvs": [
    "1",
    "0",
    "0",
    "-105854341112379836965356844298984005",
    "13004863393089789470296160259493256256960691084729025"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 253.55571926513227,
  "faltings_height": 19.02327771625049,
  "conductor": "5396999619055605101014796305076019008577308323926541422200477051902710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "29",
    "37",
    "41",
    "59",
    "89",
    "241",
    "306700111427",
    "762057475671611363423",
    "5687244150984307594789"
  ],
  "discriminant": "2848588085384977822706970819409814653720503217702910761115999942195145917806629357405166589414891520000000",
  "regulator": "2375998917746104211.55565137818131554559875077824777255834185459496606969923074",
  "points": [
    [
      "-59623723982707090",
      "138218420506792882011161795"
    ],
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      "230246921987828930",
      "-28956100975926655963759705"
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      "165517701987591410",
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      "-135158168170787967886579705"
    ],
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      "150040986983772530",
      "-22363831444324536892744825"
    ],
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      "211976007370422050",
      "9548622471470811185546855"
    ],
    [
      "3239492210957364386/25",
      "-4782863101314740184234527381/125"
    ],
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      "-359969657639359090",
      "-66820733417354976513762205"
    ],
    [
      "-2144357240355718",
      "115029748568770879857256151"
    ],
    [
      "-39262900706523310",
      "-130768823316748908387194905"
    ],
    [
      "63113187121730930",
      "-81089183630021117214511225"
    ],
    [
      "332524153188937010",
      "-120721592345284634903165305"
    ],
    [
      "234477926584306160",
      "-32801363944503226285433455"
    ],
    [
      "145453852512623410",
      "26177912679111770061300295"
    ],
    [
      "2311832550186831986",
      "3481958879121881284729237127"
    ],
    [
      "691979002698632690",
      "520672263519611379749022215"
    ],
    [
      "-250719695014802830",
      "154221593470920245344146695"
    ],
    [
      "49403486037160010",
      "-88858703803957531841581705"
    ],
    [
      "1007372537880268519390/729",
      "31155245874568914140346382161485/19683"
    ],
    [
      "-360445158421899790",
      "65804684231095531883135495"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -45/7. The 3 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 20. A two-descent gives matching upper and lower bounds, so the rank is exactly 20.",
  "created_at": "2026-08-30 01:39:36",
  "updated_at": "2026-08-30 01:39:36"
}