{
  "id": 3609,
  "curve_key": "15663233062392583790238552016:-1868476581655789129148188407059527028112064",
  "ainvs": [
    "0",
    "1",
    "0",
    "-326317355466512162296636500",
    "2162588636175573089988210707820353700000"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 194.76334090089148,
  "faltings_height": 14.166579972622454,
  "conductor": "69920387819660816126042026646958403496457502354638120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "41",
    "43",
    "53",
    "83",
    "97",
    "124633",
    "120383865861207202704904688575001"
  ],
  "discriminant": "203451294497818353546774978785472325873481688033784953253734536788817109079200000",
  "regulator": "339630882848320791620.55020667436182611174225135204122566724794105424825212",
  "points": [
    [
      "-12449942428650",
      "65539809056701272150"
    ],
    [
      "33421391609880",
      "169079712693124456080"
    ],
    [
      "265266321704840",
      "4310613681978930192360"
    ],
    [
      "41747486030347800",
      "8529929690631818858017200"
    ],
    [
      "-25384872461008975991475/2006860804",
      "5872254898510241448278768283789675/89903350297592"
    ],
    [
      "-1707664217080516767825/828461089",
      "1267736478968080443439409597726850/23845595524687"
    ],
    [
      "-150917693160043409640/11621281",
      "2570580763088509924614479863440/39616946929"
    ],
    [
      "408911916859100/49",
      "1556456625126348877800/343"
    ],
    [
      "13238843074278780/361",
      "1363479978316852767107880/6859"
    ],
    [
      "27096545514658710/2209",
      "243748926061613753193270/103823"
    ],
    [
      "237955592008571610/37249",
      "132305296003158118553971830/7189057"
    ],
    [
      "256050045710553288/52441",
      "314466738595663017498787224/12008989"
    ],
    [
      "38597866574521809990/2920681",
      "62780121303071566896044443890/4991443829"
    ],
    [
      "100835234241683867175/885481",
      "1000484315718887700735327171450/833237621"
    ],
    [
      "359086212212746841085/25260676",
      "2527821071054457690951069801885/126960157576"
    ],
    [
      "382849791711193291800/7219969",
      "7100517940874936236084062639600/19400056703"
    ],
    [
      "1357371718079790354510/93180409",
      "20117735406504191654065694982870/899470488077"
    ],
    [
      "1002158373652278405775770/147814874089",
      "919620946241976653060460186219654690/56829941196375563"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -7/20 of the rank-17 fibration of X1008, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #751 (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 19:18:37",
  "updated_at": "2026-09-29 19:18:37"
}