{
  "id": 3652,
  "curve_key": "1653344898779077780895481935881:-1607421426410476569580696637746873825818960485",
  "ainvs": [
    "1",
    "1",
    "0",
    "-34444685391230787101989206997",
    "1860441465752852048025411799379070728824585"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 208.74105971128472,
  "faltings_height": 15.413507607197728,
  "conductor": "640259658391727630453646333422455570202860388634738",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23",
    "73",
    "157",
    "193",
    "211",
    "229",
    "277",
    "307",
    "367",
    "373",
    "421",
    "457",
    "701",
    "773",
    "1049",
    "3109",
    "5381",
    "22397"
  ],
  "discriminant": "1120194582430750542556107143855195968763695868138947016775882261812725119593927140521972",
  "regulator": "219485420742320857713.64552901521859819704159046521439964807484576815",
  "points": [
    [
      "-76781306939349455370328421814791/659840790694999104",
      "1110543775663006431774936022406845081478430618425/535992533030491756533960192"
    ],
    [
      "-1174218216835538341643620996106/21998242472622025",
      "6144816327328464528471630757209817296093753613/3262736316975264771941125"
    ],
    [
      "-141045541341465820945863790968/6742298596473001",
      "887840570532414249138210864507479486797892761/553620257946591418084501"
    ],
    [
      "-2245977562098000940123373/19214949924",
      "5516547045703547265479672681155472989/2663537928565032"
    ],
    [
      "-476517116657577293025932/2291632641",
      "19608724668173730760275265345040047/109702746157311"
    ],
    [
      "182480823600648126/841",
      "52321100539808121056555705/24389"
    ],
    [
      "1465938174524165456245/9840769",
      "5778104002262919700926037543745/30870492353"
    ],
    [
      "4699889619028607022606/27363361",
      "143945466870643181129436318529675/143137741391"
    ],
    [
      "130366775420850308239119/503778025",
      "36247412233520798160998183910539182/11307297771125"
    ],
    [
      "162807514315863148801820/652444849",
      "49446516440289948701601896215426445/16665398778007"
    ],
    [
      "189883103846819741314013105/1230699578161",
      "638721991239420374690963225660297415490/1365299960324890409"
    ],
    [
      "296847449011458386133856620/48490986821209",
      "433719145574976840006896122315148237049355/337669265805869468323"
    ],
    [
      "329224857035772081857992736720/2553805351969",
      "188902835179087726689881316884730963764478115/4081141842183636047"
    ],
    [
      "1030588967292859335471214284192/30461957711727151009",
      "229249640634256358703146752280058122707497076147315/168126710695187957095764414223"
    ],
    [
      "28691445333350186047401279422467/182200791030223716",
      "45432110367023165141513838792085529573561557531/77772379592329174520147736"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -379/743, u = 11/5 of the Elkies-Klagsbrun family y^2 = x^3 + 2A(t,u)x^2 + B(t,u)x (arXiv:2003.00077, Sec. 9, eqs. (3)-(4)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:27:17",
  "updated_at": "2026-09-29 19:27:17"
}