{
  "id": 4198,
  "curve_key": "52142904825633449598241:-11536572621026439622410979290766289",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1086310517200696866630",
    "13352514607216860921549454188402"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "naive_height": 156.92482521559776,
  "faltings_height": 10.993724667529337,
  "conductor": "1305893641466358749805",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "37",
    "53",
    "89",
    "97",
    "107",
    "661",
    "3823"
  ],
  "discriminant": "5021947235420975943571743580817827086198001380263159470424300625",
  "regulator": "83638.78528174318139742384090822535161648673795278030",
  "points": [
    [
      "-64492440843080/26569",
      "-17309484833994854318173/4330747"
    ],
    [
      "-7772716885619633/206116",
      "-77769847355469814512031/93576664"
    ],
    [
      "-592271058307913/15876",
      "-2799099553421777254559/2000376"
    ],
    [
      "195507568243/9",
      "1993122037276922/27"
    ],
    [
      "-70201847276497/14884",
      "-7783034170646904489237/1815848"
    ],
    [
      "2564602194184837/163216",
      "-26610456661197981786761/65939264"
    ],
    [
      "46413988937884452/358801",
      "-9701226027493489625115461/214921799"
    ]
  ],
  "submitter": "Manvir Jaswal",
  "history": [],
  "commentary": "AI-assisted (Claude) search: Mestre-Nagao sieve over the universal Z/2xZ/4 family y^2 = x(x+a^2)(x+b^2) with (a,b) = (488395, 148148), then 2-descent (PARI ellrank, checked with mwrank). Rank exactly 7.",
  "created_at": "2026-10-12 08:26:54",
  "updated_at": "2026-10-12 08:26:54"
}