{
  "id": 445,
  "curve_key": "4361888792744213941433452103793059761:-9101435118332489552583119690411529023530688332703643625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-90872683182171123779863585495688745",
    "10534068423995936974583664932054639017801516408581081"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 253.09790556205053,
  "faltings_height": 18.862089476783847,
  "conductor": "3038587437160140161378537018221207898070176008185832826819943447344543898",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "47",
    "103",
    "15648087912489970555684237500289775534019998199017993121553"
  ],
  "discriminant": "88829305886035909223406790580188831734489544997532961921266764802355273349240637700988946188606271946752",
  "regulator": "7204154760760603178.67429124959362750014293091953483704426642506491967324350154",
  "points": [
    [
      "168995182839532794",
      "-1849047815228328206705085"
    ],
    [
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      "-14116356344573555684028861"
    ],
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      "89759888056250214764740179"
    ],
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      "-290566955614904094",
      "111383771805579971481344403"
    ],
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      "168867936408690186",
      "2021923402283802959216403"
    ],
    [
      "-348049312491962766",
      "-364651622937313662507429"
    ],
    [
      "675843549869225715/4",
      "-15174133203965767459143693/8"
    ],
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      "226743412114140666",
      "39834015980031018816673731"
    ],
    [
      "-345228833338297164",
      "-27578051745191924150290989"
    ],
    [
      "264494672967316115418/1681",
      "789406769436700456094799249579/68921"
    ],
    [
      "117088567945331298",
      "38719104511344866214092043"
    ],
    [
      "153533084142806970",
      "-14186246948927756870278269"
    ],
    [
      "4705528746139000386/25",
      "1237790742135157721822446119/125"
    ],
    [
      "283719461313430458",
      "87121807406646082412817603"
    ],
    [
      "156725078089691856",
      "11901217671025861648745403"
    ],
    [
      "187535709998017620",
      "-9367985213511861833743719"
    ],
    [
      "169343824650362106",
      "1292130346674654571447491"
    ],
    [
      "677728207348789695/4",
      "-8931655065396010855482123/8"
    ],
    [
      "-339654662569037526",
      "-47064215388506264365852125"
    ],
    [
      "390844227572272218",
      "-186338563793494941720656637"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 22/5. 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 15:54:59",
  "updated_at": "2026-08-30 15:54:59"
}