{
  "id": 3994,
  "curve_key": "12234521798916338425:-134040949609491247111643018125",
  "ainvs": [
    "1",
    "0",
    "1",
    "-254885870810757051",
    "155139987952707713441282998"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "naive_height": 134.13588571641293,
  "faltings_height": 9.232129615834738,
  "conductor": "145059433532653065217081920420450",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "41",
    "53",
    "61",
    "103",
    "109",
    "263",
    "353",
    "443",
    "619",
    "3931",
    "31069"
  ],
  "discriminant": "-9337771897686435317629091295333931508053694494059750000",
  "regulator": "8801521254112256.0355955079841086995640143897429828106112984496",
  "points": [
    [
      "-2833944860783/4096",
      "140682543539544359/262144"
    ],
    [
      "-11668950907991/40000",
      "114451437732138228127/8000000"
    ],
    [
      "1264039903243/2209",
      "1455924235353984328/103823"
    ],
    [
      "1007376152",
      "30341976774861"
    ],
    [
      "105456773552",
      "34245704359029186"
    ],
    [
      "629124230762063/546121",
      "15047998697400783044268/403583419"
    ],
    [
      "-5984376377743/10816",
      "12666286219016170779/1124864"
    ],
    [
      "11935674245707/74529",
      "221417400052477941304/20346417"
    ],
    [
      "798726167588321711/113827561",
      "712139797358894794278280404/1214426248309"
    ],
    [
      "129510118251671768/232593001",
      "48357753878032680317444367/3547275858251"
    ],
    [
      "-46304796115758292852952/89755861237849",
      "10391430431677528251912071617460473/850343169865348198493"
    ],
    [
      "1706080145352527730407/742476912241",
      "69206776773528806397860736483996/639770823447614711"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3629 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 12: 12 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 04:41:38",
  "updated_at": "2026-10-05 04:41:38"
}