{
  "id": 1927,
  "curve_key": "49698883141214820224180514156049:282484451000051306587922278711700060720472958343",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1035393398775308754670427378251",
    "-326949596064874283722508090895752774295421519"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 218.9506057519911,
  "faltings_height": 16.252931081834785,
  "conductor": "30028829356595171319917435366264454669457035196770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "109",
    "139",
    "229",
    "337",
    "373",
    "601",
    "1279",
    "2251",
    "2671",
    "2857",
    "6781",
    "15289",
    "146677"
  ],
  "discriminant": "24859798555573819912874887871678366552183915396453418330851394828457954697888784564131160000",
  "regulator": "6195514592256.214920766075012282534080847804528916234829444887898",
  "points": [
    [
      "-1494959723630561/4",
      "-22362386440211928980539/8"
    ],
    [
      "-235900658781491755352566/445505449",
      "-80252254262482004708478021258819869/9403283512043"
    ],
    [
      "1843380435284780",
      "-63469111459583693423791"
    ],
    [
      "196315756356652181/16",
      "-86675315018928737462257537/64"
    ],
    [
      "8746899183529396706/5041",
      "19929554356036165519680007987/357911"
    ],
    [
      "-480400624438210",
      "7719125608406182934201"
    ],
    [
      "-63967273046799675792296785084/82601722925401",
      "2426885002075265453339411099526703693782383/750729806291930333149"
    ],
    [
      "1622410358882474",
      "-47578892302856415340147"
    ],
    [
      "92477112989087639510843384120/53260789404001",
      "-21676087513129361220487017233141697121824409/388697187809609893999"
    ],
    [
      "-1036508675669164255299090971591217095333340484/1421881062783081067608776365801",
      "10783156118017713199466391879565357925784129072442447486101135897167/1695488721642054229514120237427879872836163701"
    ],
    [
      "174993160882297690664342516477838099770672009092781610632394356786/21863106349491622054082031405713336780451274695721",
      "-72585973312810890648572199826318709248688186485072026930812102791003613528409027459749141783930423/102227514327673429971749969985901000527303034094780020664770512337168544981"
    ],
    [
      "-376982951501591962494110882302/530033157957601",
      "86002456399142170780875142892517484967181973/12202661347387813184849"
    ],
    [
      "-103549726811848385005926692048425820318807995396/280792813162255321581643377563569",
      "-10229742011200547151410140879826694859272057682466333244724174562733799/4705209680594895605903242244060163545233276747753"
    ]
  ],
  "submitter": "Alvaro Lozano-Robledo",
  "history": [],
  "commentary": "Rank exactly 13, torsion Z/2Z: 13 independent points; 2-isogeny Selmer bound 13, confirmed by a second 2-isogeny descent. Specialisation of Kihara's rank-8 family (S. Kihara, Proc. Japan Acad. 77A (2001) 11-12) with u = (s^2 - l)/(2s), (p,q,s) = (5,13,575/3).",
  "created_at": "2026-09-25 19:16:35",
  "updated_at": "2026-09-25 19:16:35"
}