{
  "id": 6329,
  "curve_key": "1550131260478315744:1490653435150891360823942528",
  "ainvs": [
    "0",
    "1",
    "0",
    "-32294401259964911",
    "-1725293338485739495016015"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 125.6546138562541,
  "faltings_height": 8.486252829334099,
  "conductor": "562432500597433744639469518241920",
  "bad_primes": [
    "2",
    "5",
    "11",
    "31",
    "47",
    "89",
    "97",
    "191",
    "617",
    "769",
    "823",
    "1367",
    "2777",
    "22433"
  ],
  "discriminant": "869660576556062388193774936136010900347200665440000",
  "regulator": "27102055932.266890772139353754816590706802797274432989686369436",
  "points": [
    [
      "-74041568",
      "509830865225"
    ],
    [
      "205540911",
      "-566026943504"
    ],
    [
      "742622401",
      "19591822955474"
    ],
    [
      "-98786639",
      "-707759120854"
    ],
    [
      "41691717832",
      "8512765009714475"
    ],
    [
      "66497169897/121",
      "-16110377765262850/1331"
    ],
    [
      "430909980429/2116",
      "36860640985321021/97336"
    ],
    [
      "-2012025215/16",
      "37711760818985/64"
    ],
    [
      "47764061736",
      "10438757271772229"
    ],
    [
      "1509691562737/6241",
      "-1059457141684930150/493039"
    ],
    [
      "-122681776",
      "624643959039"
    ],
    [
      "1410229751",
      "52510224817524"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rank 12 curve with rational 2-torsion (torsion Z/2) from Layr-Labs elliptic-rank-challenge-public, file submission/board/z2-r12-s.ec, commit a066c9ff5312fb736e666731855b7cc6b39dabc1:\r\nhttps://github.com/Layr-Labs/elliptic-rank-challenge-public",
  "created_at": "2026-11-01 01:10:28",
  "updated_at": "2026-11-01 01:10:28"
}