{
  "id": 3618,
  "curve_key": "1415960312299495081:-7185685618891229002015038229",
  "ainvs": [
    "1",
    "0",
    "1",
    "-29499173172906148",
    "8316765760147324691627078"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "naive_height": 128.28377689892588,
  "faltings_height": 8.746639120535935,
  "conductor": "10817942205250900617851910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "61",
    "83",
    "131",
    "191",
    "229",
    "349",
    "359",
    "479",
    "991"
  ],
  "discriminant": "-28237938217034303011063296998709996320882204124592500",
  "regulator": "27523467486.63984306211591136005078339963832103979406588762",
  "points": [
    [
      "29130763",
      "2735337832913"
    ],
    [
      "112851499",
      "2534693206115"
    ],
    [
      "172231504",
      "2888702716130"
    ],
    [
      "459906724",
      "9592824727985"
    ],
    [
      "25147710946/25",
      "3945808286721691/125"
    ],
    [
      "26821198513/49",
      "4286317835939411/343"
    ],
    [
      "30421158913/529",
      "31751877436170379/12167"
    ],
    [
      "103423438693951/124609",
      "1036793371170365156275/43986977"
    ],
    [
      "2788252446514099/1371241",
      "146775891974810817532385/1605723211"
    ],
    [
      "311790935011846561/49729",
      "174098544242564675071780715/11089567"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 26 of the rank-9 fibration of X400, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #802 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:20:36",
  "updated_at": "2026-09-29 19:20:36"
}