{
  "id": 6336,
  "curve_key": "8297398731419191744:-22637002165538514474287452672",
  "ainvs": [
    "0",
    "1",
    "0",
    "-172862473571233161",
    "26200233930270974636310535"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 130.68742120116116,
  "faltings_height": 8.83282641961407,
  "conductor": "562432500597433744639469518241920",
  "bad_primes": [
    "2",
    "5",
    "11",
    "31",
    "47",
    "89",
    "97",
    "191",
    "617",
    "769",
    "823",
    "1367",
    "2777",
    "22433"
  ],
  "discriminant": "34036861834781909171364361307426912578577093876326400",
  "regulator": "111010021098565.18460268279297972875553506425763607752575536921",
  "points": [
    [
      "340247954",
      "-2602726313561"
    ],
    [
      "18333237329/64",
      "-222312853321223/512"
    ],
    [
      "37945908674/49",
      "6478523366534407/343"
    ],
    [
      "159897395354/289",
      "49112044163398973/4913"
    ],
    [
      "41692389866",
      "8512628256843781"
    ],
    [
      "71416794794/121",
      "-15163089232470809/1331"
    ],
    [
      "603068163629/2116",
      "28181630495659421/97336"
    ],
    [
      "25840787585/16",
      "-4027267003277015/64"
    ],
    [
      "47764648586",
      "10438629396570379"
    ],
    [
      "1966848663434/6241",
      "-857253355946942171/493039"
    ],
    [
      "12060670066/9",
      "-1266716367786997/27"
    ],
    [
      "14860477063429/10404",
      "55073984887123761817/1061208"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #6329 (Layr-Labs elliptic-rank-challenge-public, submission/board/z2-r12-s.ec, commit a066c9ff5312fb736e666731855b7cc6b39dabc1). The twelve points of #6329 were transported through the exact Velu 2-isogeny on its rational 2-torsion point and checked exactly on this minimal model; independence re-certified by reduction mod 3 and mod 5 at 80 good primes each (torsion Z/2). Rank >= 12 is preserved under the isogeny.",
  "created_at": "2026-11-01 02:17:08",
  "updated_at": "2026-11-01 02:17:08"
}