{
  "id": 3977,
  "curve_key": "4306211708425661366020753988136913:174632379850427827451036188621638396129522831926855",
  "ainvs": [
    "1",
    "0",
    "0",
    "-89712743925534611792099041419519",
    "-202120810012069252211057582477002830047053025616"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 232.33609989735322,
  "faltings_height": 17.400898072938965,
  "conductor": "1319483920430920599678754550348754589797",
  "bad_primes": [
    "3",
    "19",
    "61",
    "71",
    "97",
    "167",
    "229",
    "269",
    "443",
    "449",
    "773",
    "1229",
    "1823",
    "1997",
    "2731",
    "2851"
  ],
  "discriminant": "28562264678516369242872664169896291489456887940749513934695788509892290354472895131671025763221649",
  "regulator": "79823936291445081.6354376127476915163320581662648782941578244",
  "points": [
    [
      "-45167134881508859734212/7038409",
      "6173909876107188868171022166702318/18672899077"
    ],
    [
      "12391172860869862430193888/1203409",
      "43618270304021154152724715092325766652/1320139673"
    ],
    [
      "-90389865752547635664385671/28927206400",
      "1074507868951337225960725381991185990173/4919939264512000"
    ],
    [
      "-487224045725521773972973167/62244262144",
      "-2223766067821361037535280357717811206817/15529196473782272"
    ],
    [
      "30793926678244902447657/2483776",
      "3010125930241612446546242500062249/3914430976"
    ],
    [
      "4237395860559295484453062563/272887132996",
      "208970492208231121385142173454188598059031/142552417857248456"
    ],
    [
      "843959009222994276005433445301244/48959844237751225",
      "19897535010767064413985924325613657548000408306842/10833281821087368045425875"
    ],
    [
      "97310457949945858043393524463244/7049805016355689",
      "645575979471670847361970680647545453898321773986/591923603415459629122613"
    ],
    [
      "654112810099904985281315380820307439308/4472683226456764196761",
      "-16693682173723707237783527688953999622232043283942668284974/299124655295884767664888482455741"
    ],
    [
      "-205848566783670426806250417579483/84970218840138256",
      "782788897533458303888524954144154328343028085429/24768522755657862582316096"
    ],
    [
      "-12044804644761738691114914679623/4709931954555136",
      "-33246097684155456758089416730593240351448924149/323237656352974973456384"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3702 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 11: 11 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 04:38:08",
  "updated_at": "2026-10-05 04:38:08"
}