{
  "id": 4012,
  "curve_key": "60608901834857474164133798425:2667160791223441695273756024999344223071875",
  "ainvs": [
    "1",
    "1",
    "0",
    "-1262685454892864045086120800",
    "-3086991656509139192173052611175434290000"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 198.82271786427341,
  "faltings_height": 14.634830139368677,
  "conductor": "46743260634842018618863285423770046153816518554850",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "29",
    "67",
    "139",
    "239",
    "313",
    "523",
    "811",
    "1193",
    "1571",
    "2953",
    "12113",
    "14281",
    "63709",
    "127691"
  ],
  "discriminant": "124727636543723156990691670384991642883485394994795766939633076131809640464790250000",
  "regulator": "2484293956256037936031635.5762896193234950259147645999820893353841486",
  "points": [
    [
      "1037102328639676635740/9409",
      "33398917488790106680836471693760/912673"
    ],
    [
      "-10136958476130015536079815395937680712382850340/1068342058653494076965126440576201",
      "3131022775622438737198741418680559022870384618192546681246216693956480/34919296783440236155188988830222872571535598626949"
    ],
    [
      "-104618473051427647296701372813895721511/8322615714954811530702121",
      "2495080066378339243690221485788818454604989998657083468810/24009867492220776481239205723615509419"
    ],
    [
      "-2160862062801073060/104329",
      "4012864344124257436593479040/33698267"
    ],
    [
      "2127280057346433004863654664/11787857889025",
      "96168215111873025196059140794596322746748/40471782943994538625"
    ],
    [
      "333989116917770464131656/319515625",
      "192906470164489702145178352252206804/5711341796875"
    ],
    [
      "2883638801196029309159802385/78405782927616",
      "-10338904807862750510995965641984011221695/694259999712293105664"
    ],
    [
      "-280308451551952001347243095827606912711/8186042659708454348403649",
      "-7215503031630818502734394948437483229908277569023157942/23421300451899721704421238331801218143"
    ],
    [
      "-813829500393866288432144822170023215/33433341287446652978176",
      "-703044522459237836262441252665029480952165100986372105/6113215033303562062620669948952576"
    ],
    [
      "51930706535931669395608504812959352889/113319410431916446539769",
      "373095310391984605766637962802230556315767254278295559434/38146654818054272798864135299855603"
    ],
    [
      "9187008648112594198773896/242324830225",
      "-7090984724464570537712969741803564164/119288032550709625"
    ],
    [
      "45754530062314167283921554349241660/338845225050960404401",
      "-9435710354050444120761949037843923875596833845997020/6237377869190007360649163164649"
    ],
    [
      "19801619048241017878554651064739997385985/317539039578388786254981361",
      "2268117400700452670857073023700171364347724048593210266168455/5658426647686689944530315510693649090359"
    ],
    [
      "313869958193281798650754310419369650782684/8254249169834838438111617929",
      "-46715789880734367633841882857484108144040750437128990536457088/749922462201671742931942518452938206357467"
    ],
    [
      "185047193469173610637807816422589738682065/4113429440399242565587109569",
      "46562629008380707088122435037867945429199543254530984374506110/263819005010491421832123254548499902750753"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3647 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 15: 15 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:45:26",
  "updated_at": "2026-10-05 04:45:26"
}