{
  "id": 3702,
  "curve_key": "1828504967871942387027989423619553:-76204613509207681558078543368451760264088933326065",
  "ainvs": [
    "1",
    "0",
    "0",
    "-38093853497332133063083112992074",
    "88199784154175554184399411528400670974658330899"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 229.76642023295463,
  "faltings_height": 17.05432448265899,
  "conductor": "1319483920430920599678754550348754589797",
  "bad_primes": [
    "3",
    "19",
    "61",
    "71",
    "97",
    "167",
    "229",
    "269",
    "443",
    "449",
    "773",
    "1229",
    "1823",
    "1997",
    "2731",
    "2851"
  ],
  "discriminant": "177277782467817619005821047502012637191550394064348783530030994123011715920672477534313338060209",
  "regulator": "38976531392307.1687673035218494587482090127764965226045692502",
  "points": [
    [
      "-5310464569348647",
      "375146976376325132054286"
    ],
    [
      "10296725098306694091",
      "33040651263419675043419030637"
    ],
    [
      "-27802195024064466/25",
      "44928438178283668606176813/125"
    ],
    [
      "785925785633371521/256",
      "55843213147838387322557847/4096"
    ],
    [
      "27066979206514374515241/2483776",
      "3849726960380461353919913379920937/3914430976"
    ],
    [
      "73124567577145251930435/5026564",
      "18216246652039118342066966235034719/11269556488"
    ],
    [
      "154307259892345172097993/9406489",
      "56810793830789906878562425867560162/28849701763"
    ],
    [
      "503771472284577295518621/39980329",
      "320642625056309607030537409278390678/252795620267"
    ],
    [
      "1109318675257309848511245/271227961",
      "127417955895339245008868378026430202/4466853289709"
    ],
    [
      "358160944219148399763989517/610729746064",
      "122672606630805006769914089309217570706953/477280410711047488"
    ],
    [
      "586175666644057801225865217/411383697664",
      "50625906464648635936263285138555377649513/263858212612108288"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 46235/147474 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:46:09",
  "updated_at": "2026-09-30 01:46:09"
}