{
  "id": 429,
  "curve_key": "170322235137624986266645072570161:-2243155666655675344521322360695115559704473068841",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3548379898700520547221772345212",
    "2596244984555180683994653333342076110656596799"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 222.66393623587788,
  "faltings_height": 16.416087279042546,
  "conductor": "3294048358302772938894219727593961593965230803928008677606014515626270",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "31",
    "1968749",
    "92346409",
    "1423034287",
    "104937741999596607860891696642716903961"
  ],
  "discriminant": "-52521162535382074717439043300866350950112927203157501676552632309040698338202829093120000000",
  "regulator": "10087907745235037808.4720051819669974776346184561148590643753324148278639580912",
  "points": [
    [
      "3208068410526357",
      "155657592404062027312421"
    ],
    [
      "1095482427449557",
      "-4870896459426844043579"
    ],
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      "1855942811805097",
      "-49025441849159211750179"
    ],
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      "-20217361031895494895579"
    ],
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      "973548032736657",
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      "458554162517225327/361",
      "80716916851009337797211639/6859"
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      "916575819015157",
      "10672928533516225548421"
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    [
      "1324306440467157",
      "-14820755597628058891579"
    ],
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      "595473871966197",
      "26351964156054766354821"
    ],
    [
      "1439056872582357",
      "21680528321812318785221"
    ],
    [
      "-1739162520750563",
      "59220211184259972033421"
    ],
    [
      "50652444939397",
      "49159341147838724774821"
    ],
    [
      "127771885628597",
      "46313580597341706074821"
    ],
    [
      "887669226338657",
      "-12078999566166863412079"
    ],
    [
      "5160109421258096573/4489",
      "-1811451714849670882603148377/300763"
    ],
    [
      "103285830196582117/81",
      "-8775603785644593513829091/729"
    ],
    [
      "1022925801399957",
      "-6073044553877013864379"
    ],
    [
      "524045495469797",
      "29675710101367413054821"
    ],
    [
      "1030447959551157",
      "5829021636357064948421"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 25/13. 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.",
  "created_at": "2026-08-30 01:39:35",
  "updated_at": "2026-08-30 01:39:35"
}