{
  "id": 3972,
  "curve_key": "31494534857761579681:94546823720221972529828716175",
  "ainvs": [
    "1",
    "0",
    "0",
    "-656136142870032910",
    "-109429194175305294926471164"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "naive_height": 134.68903712427942,
  "faltings_height": 9.272116781820692,
  "conductor": "58287634249314930726735678",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19",
    "31",
    "67",
    "83",
    "101",
    "107",
    "163",
    "199",
    "211",
    "283",
    "1171"
  ],
  "discriminant": "12905386333681135856517646882479550937055476765118569472",
  "regulator": "2015294999873.294394557022458575689178141604534440680310125",
  "points": [
    [
      "-491154214",
      "9713766935648"
    ],
    [
      "-22427769230194/32041",
      "-15052297725007339646/5735339"
    ],
    [
      "7785084920684/2809",
      "-20715039164829785798/148877"
    ],
    [
      "119612007239/100",
      "-28584615335599483/1000"
    ],
    [
      "32896234844/25",
      "4516440483365818/125"
    ],
    [
      "-15777657964/25",
      "912589643223394/125"
    ],
    [
      "-255966851637608/1292769",
      "5243056057286125938562/1469878353"
    ],
    [
      "-391880094530221/2220100",
      "-3118115983812042339713/3307949000"
    ],
    [
      "6749479935587666/6754801",
      "-267749538154405062108136/17555727799"
    ],
    [
      "24892807799998496/7722841",
      "-3794811227902199615959078/21461775139"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3619 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 10: 10 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 04:37:03",
  "updated_at": "2026-10-05 04:37:03"
}