{
  "id": 414,
  "curve_key": "20059808396298664990881291611514389102251644001:-2310571076957343669899179397873955432962058129973461274037466023466001",
  "ainvs": [
    "1",
    "0",
    "0",
    "-417912674922888853976693575239883106296909250",
    "2674272079811740358679570958520093732597884037078754632469690562500"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 319.84514224706925,
  "faltings_height": 24.65897356158845,
  "conductor": "16760725130923377828936183343653472405052507400204269535633169891162525316371894847775702540918638174274090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "29",
    "31",
    "107",
    "2389148369575121535136373159566497236058454879555115678910972748319347864775402115477928908335141"
  ],
  "discriminant": "1581739705138847952897657581979669295980470647074499285199050633127943304037864743566952295543770172880782758840137269478960433920000000",
  "regulator": "3932032436300986209338186096.240109828705554754518125658728216810084174523195871294191491",
  "points": [
    [
      "15822380316923547828580",
      "151643060249117670730726936276270"
    ],
    [
      "-22816408878790378304900",
      "575828230148625383476004261500750"
    ],
    [
      "3502597587318607010039500/9",
      "6546290214313260910388604210152505250/27"
    ],
    [
      "-12847639393307369174300",
      "-2433682077246885894706777800506450"
    ],
    [
      "37368154869795085727692",
      "6264004564904152704618026454846502"
    ],
    [
      "-8147032401957697531268",
      "-2353352489348946565146929622436298"
    ],
    [
      "7314863982403396321060",
      "-93251557207261203580730036421650"
    ],
    [
      "15878183809166079843600",
      "-204287664445226886637292709486750"
    ],
    [
      "6276682928817426954072556",
      "-15725084384127481121029416422467664498"
    ],
    [
      "17105485255858886411800",
      "-728489777122742608029142376831750"
    ],
    [
      "3466564719651636987652",
      "-1125703646276725605809873386784498"
    ],
    [
      "191318624420912972948980",
      "83219710469615739584503837268461870"
    ],
    [
      "1088549103290770089465850",
      "-1135522877485039954086011907487005500"
    ],
    [
      "748748481806784583411555/4",
      "644151500019090092797555295593415075/8"
    ],
    [
      "15765778007347823814550",
      "65509983713733457724183865693250"
    ],
    [
      "7027681705713219135600",
      "-290517027792982258106875094586750"
    ],
    [
      "54104839457060278926340",
      "-11766311708087028814291592566257650"
    ],
    [
      "7795942312580552683974204100/1129969",
      "-415032435232650929609295747255897247543550/1201157047"
    ],
    [
      "1855795325004069684186400/49",
      "2200868019361747716785742237904337950/343"
    ],
    [
      "3558348719572905341759424148/214369",
      "55340098718074725998937110659283186702194/99252847"
    ],
    [
      "1124939783631397150741848478974625/330790620736",
      "216284368675656747861486004558093648562126796669125/190252240772585984"
    ],
    [
      "357805967957512958460505193065/48888064",
      "-29920995894753812033971276258593973961533075/341825343488"
    ],
    [
      "10348737837123444886619656146347740/7375889689",
      "-1052652882191382866990397839697257143810371738739870/633463534160387"
    ],
    [
      "46702079872170180690148303697500/2900576449",
      "54003469752825789415439788310295350829323449750/156216345813793"
    ],
    [
      "5654320077321690108631172995/37636",
      "-421392451679890918317802354675473245564005/7301384"
    ]
  ],
  "submitter": "7fff-zip",
  "history": [],
  "commentary": "Found in this search by specializing Noam D. Elkies's rank-17 elliptic K3 family (arXiv:2608.25406) at t=-216/329. These 25 rational points are certified independent exactly by Cremona-Brumer quadratic characters; the claimed lower bound is rank >= 25.",
  "created_at": "2026-08-29 05:03:40",
  "updated_at": "2026-08-29 05:03:40"
}