{
  "id": 810,
  "curve_key": "25559594097550338486898411584671332959856801:-129065813360139172644994843092569264056463089916537869134816025201",
  "ainvs": [
    "1",
    "0",
    "0",
    "-532491543698965385143716908013986103330350",
    "149381728426087005376107064469239512209181414698102849693722500"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 299.8487599642669,
  "faltings_height": 22.76740245548319,
  "conductor": "1378397082251839370263140297286229416548691765876717448982399683310777484953385725077098223803466345145690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "37",
    "666229087",
    "16936652169366103",
    "1489030358063875190255171533",
    "17601544640376275918143047501174198706494809917"
  ],
  "discriminant": "23099482376905988457966054201887058788535363928898683076895413572182222503235231396509690958038250558023605895963900774400000",
  "regulator": "417759432785830517182243520489876.4116138352584306207496146142877126157272764143668378380",
  "points": [
    [
      "909117052465725803260",
      "-20412354269520390940209323216510"
    ],
    [
      "288584445201706457650",
      "4443708777781628474716304792200"
    ],
    [
      "-1955306005496150183300/9",
      "430998386184755400706453084942550/27"
    ],
    [
      "602300360660721077500",
      "6867008539101162976085264171650"
    ],
    [
      "643944123233651777500",
      "8573645426318872538838356171650"
    ],
    [
      "160684573168093693630",
      "8244231467966299314661028532070"
    ],
    [
      "537592524816391739620",
      "4299484989696686381887481870050"
    ],
    [
      "433850517183061130050",
      "148532589737624087218767900550"
    ],
    [
      "451976127109096771300",
      "1019332908183239607975647150650"
    ],
    [
      "87304763654441914587580",
      "25795371655594326994545201062210050"
    ],
    [
      "2199497585098921897135/4",
      "-38232386659749252423458018243875/8"
    ],
    [
      "8275754486899609397500/49",
      "2749681567790306156963357907875950/343"
    ],
    [
      "25254975871866664415260",
      "4011816746699707529463705943953250"
    ],
    [
      "-2403530799301581998195/16",
      "962094887728520625484636605166075/64"
    ],
    [
      "1776924048110510039203/4",
      "5642969601454184299749489927203/8"
    ],
    [
      "129053923539548578351150/289",
      "3939611312512020864490956207795500/4913"
    ],
    [
      "588565463465583424090780/9",
      "451507780687142071225219023903695350/27"
    ],
    [
      "361399592272156613211584099317308902158042770692484100/1424348406562308153354190137953449",
      "297398594309579399002665654102656863133462329562366794626124443594659176998416450/53755678900038047314285515018101565307351626822293"
    ],
    [
      "18464239219544991560097369042158751603292040048153297680/33971387448806191711822093996867129",
      "28367905274622673546705585859748071490893941434251041583923747493636715454765084490/6261378055524211651057143381008101280895045650788883"
    ],
    [
      "1956503551675276404316971121201599793363608874145314780/3383768891911755998497734985268889",
      "-1161112108539894538828195615611202847454665838639040142738948915974567582590771910/196834417909836830647489378375908442526775433809213"
    ],
    [
      "55664881434709262431670574877823714713921366267686839020/110270370143037103760562402321181321",
      "111159823490030489951177671032328281006034130964747569966957264079160871030620333450/36617462759740868240460575249777941769476816167368869"
    ],
    [
      "13560296405081088889082518543068156591236525253831268150/43890580129600724386627435632502561",
      "34839745044919031589623930300891464450750950463511662365992578329828103664984167450/9195111118422108933214727349957944902785510661514191"
    ],
    [
      "37030392758459178914790112353104932923117815558645657260/101176626171287207105354385593825569",
      "60363026328139735875075702592111052263042874185186231196974340081752455044746633250/32182537949356988799769820736976139061870517051688753"
    ],
    [
      "-552466623201962561540231964327573126623645286350237485250/966144059466377549017678838420375761",
      "15514347624315989400281757516947653260133220889856538307068664768076836212672533159900/949648380197523963087703181995085660149087410104602009"
    ],
    [
      "192872541138606215882460549687834397883326961391973249660/2187052857228956834576359611054708841",
      "32842423302303246089519047018871422940318619515305388734157054517312668394970634493110/3234364182462051896657024024701189509489665239019416139"
    ]
  ],
  "submitter": "hdeping",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-21 01:38:41"
    }
  ],
  "commentary": "Specialization at T = -15/604 of the genus-one fibration with 17 independent sections behind the rank-30/31 records #273/#302 (the 'wgxli' family y^2-(Lx+B)y = x(x+D)(x+E)), with 25 independent rational points.",
  "created_at": "2026-09-21 00:10:47",
  "updated_at": "2026-09-21 01:38:41"
}