{
  "id": 3635,
  "curve_key": "69595489595398579710481:-14751578322728624974524340041600121",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1449906033237470410635",
    "17073586021555823773300048810225"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 157.79096014035483,
  "faltings_height": 11.157007127908763,
  "conductor": "8517544174435024143004460515381044430",
  "bad_primes": [
    "2",
    "5",
    "31",
    "151",
    "193",
    "199",
    "241",
    "311",
    "409",
    "1031",
    "1721",
    "2333",
    "2437",
    "2711",
    "5651"
  ],
  "discriminant": "69142899231148177935060350089607447124329289768529170022400000000",
  "regulator": "834237764991718.7028386439467062690949270563631122265203157966983",
  "points": [
    [
      "642998256463902",
      "16304770252901039521441"
    ],
    [
      "-1082604861778690/26569",
      "12626439696697732579755/4330747"
    ],
    [
      "-1028345520020370/24649",
      "8609367015441893855045/3869893"
    ],
    [
      "-36302761587770/8649",
      "3864715856739211216405/804357"
    ],
    [
      "774552365845/16",
      "497106550180425535/64"
    ],
    [
      "19379923473630/2809",
      "404954673922084296605/148877"
    ],
    [
      "52091107629310/9",
      "375955046155281021115/27"
    ],
    [
      "2402155348381470/196249",
      "93641309059065339504355/86938307"
    ],
    [
      "71270177161463070/1739761",
      "11796061363856241089249335/2294744759"
    ],
    [
      "158193677749124270/5248681",
      "10432987622587004418638315/12024728171"
    ],
    [
      "2237332065773628670/69239041",
      "1146781850352455313960446465/576138060161"
    ],
    [
      "3783959112265361330/344213809",
      "10022791775877118878197219505/6386198798377"
    ],
    [
      "1061577159127196192270/29580216121",
      "17072488116289920360218086341485/5087471790434669"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -31/84, 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 19:23:54",
  "updated_at": "2026-09-29 19:23:54"
}