{
  "id": 3644,
  "curve_key": "3787555408083654065200752336:-211516224697410037432456350837052386235584",
  "ainvs": [
    "0",
    "0",
    "0",
    "-78907404335076126358349007",
    "244810445251631987769046702357699521106"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 190.50455493229416,
  "faltings_height": 13.845344108128542,
  "conductor": "85468703986756648905003803597594316557982840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "47",
    "53",
    "61",
    "97",
    "103",
    "163",
    "197",
    "313",
    "463",
    "607",
    "1171",
    "1217",
    "3041",
    "8377",
    "138637"
  ],
  "discriminant": "5552980633313668063359952530705317287553254923137131483475260420280240443296000",
  "regulator": "2104530733248798709.57635954818376240705891501143631304608926421270",
  "points": [
    [
      "-679675943687593800853941238/119661917902081",
      "29553881562765542263884969061170708489990/1308982796888125177729"
    ],
    [
      "-135775740826118032437091/13491519409",
      "6948362274532410760054298569674630/1567080453913577"
    ],
    [
      "-1599417649145057683/18826921",
      "1295535860834753298897047944890/81690010219"
    ],
    [
      "-1856179014986249/225",
      "61709955644330587195624/3375"
    ],
    [
      "295607188568239005/24649",
      "123796264379260096010671178/3869893"
    ],
    [
      "1038421764728299475/312481",
      "767144888123031739639862136/174676879"
    ],
    [
      "1474502765858785523/61009",
      "1681764377313739648509090720/15069223"
    ],
    [
      "45261172645900978313/12020089",
      "43248969389478416283583793910/41673648563"
    ],
    [
      "65594323425857585847/9728161",
      "133343636363483050264209423160/30342134159"
    ],
    [
      "8876841522447891822422/653364721",
      "684652769769518007350901032335320/16700655633481"
    ],
    [
      "359019745624300468239981/53111350681",
      "55145114201350709078818066465444870/12239988766592579"
    ],
    [
      "501062001074119247745227/161518681",
      "354678958127999803303180592833529520/2052740916829"
    ],
    [
      "826668655699504704280778/36215231809",
      "700717744950292015405151027839078410/6891867258948127"
    ],
    [
      "1503303702102022779812417/230568990976",
      "303215820856520007076556583841153695/110713695810891776"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 31/225, u = 2/5 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 19:25:46",
  "updated_at": "2026-09-29 19:25:46"
}