{
  "id": 4007,
  "curve_key": "-293026117502982927181471402143519:-305809961754685220340043401004204954583163254565585",
  "ainvs": [
    "1",
    "-1",
    "1",
    "6104710781312144316280654211323",
    "353946714993848633126650315093497433178867991805"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 232.49409666544796,
  "faltings_height": 17.43226177400362,
  "conductor": "373194485014698697229027713931389442079902239969278",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "31",
    "37",
    "59",
    "109",
    "167",
    "181",
    "283",
    "983",
    "2221",
    "3163",
    "6563",
    "7867",
    "43117",
    "859378921"
  ],
  "discriminant": "-54134776153059133501420672633602124938975215355076407431250557480000984894622684760816771328252928",
  "regulator": "1011444653885273516041.8784619964848407382891778214483828714801724055",
  "points": [
    [
      "-441811123760373495883685/77986561",
      "255412220283973888047536833591682044/688699320191"
    ],
    [
      "54395050265588755583/121",
      "401186655358025562744874634552/1331"
    ],
    [
      "-197384667663581097665/66049",
      "9436003247033217309030157897312/16974593"
    ],
    [
      "2516095934557143239/3025",
      "99769506854052611501815044152/166375"
    ],
    [
      "193317138062976051103819/990025",
      "85006203628906580606182601176973188/985074875"
    ],
    [
      "167942349464404835591801831/105089430625",
      "20660219800609705684704722267572135508704/34067366172859375"
    ],
    [
      "-2036943370568251645487729/13536159025",
      "935719529788409734492377823417338858784/1574864421763625"
    ],
    [
      "20683222907054356904815/85544001",
      "471699677247995783524965814950694016/791196465249"
    ],
    [
      "362899264801456834825/10816",
      "6964148322268371914528852363641/1124864"
    ],
    [
      "10578883651569284352708295/60357361",
      "34412575677194298333897179289510097576/468916337609"
    ],
    [
      "12519753700662537506695/10452289",
      "20359023224574514400440598334121240/33792250337"
    ],
    [
      "63591086973100364818903/10201",
      "16035939427251734000060596694096512/1030301"
    ],
    [
      "-112148089910529154703725/39212644",
      "137396704272068338796450020603347107/245549576728"
    ],
    [
      "56030894639447366144255071/7154622225",
      "568369388941155889932685809820662866576/605173720901625"
    ],
    [
      "7873221415432301208162598056409117/119390001669987889",
      "699521021057457053923786238423325706396737786026258/41252658101398548913331287"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3651 (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 04:44:28",
  "updated_at": "2026-10-05 04:44:28"
}