{
  "id": 4643,
  "curve_key": "4772892343933469856657581261806272900132496:-10364443551142504403395394712055522167750463950168678731245771456",
  "ainvs": [
    "0",
    "1",
    "0",
    "-99435257165280622013699609620964018752760",
    "11995883739748268985378191386564723783114025998377130895653908"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 294.814579164897,
  "faltings_height": 22.411495685504896,
  "conductor": "12437980303867946022779738389472071607816438224008357360",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "43",
    "47",
    "53",
    "59",
    "61",
    "71",
    "73",
    "103",
    "151",
    "181",
    "571",
    "607",
    "853",
    "1627",
    "1657",
    "4241",
    "23929",
    "24071"
  ],
  "discriminant": "756475838384846306411404854972231958880719207616893514885793182318648285224885027809180961142297533074833089591708224000000",
  "regulator": "547265061691.82923750425841607816903340261791761337443652866217",
  "points": [
    [
      "167385317948221952686",
      "204101546508351336343067805600"
    ],
    [
      "161337559769180883511",
      "390931872175009353829503545250"
    ],
    [
      "-309812336698634859164",
      "3614584858107150170418441616350"
    ],
    [
      "202005801306169330486",
      "390516463003494440227652692200"
    ],
    [
      "224866462883959490071",
      "1003287227001190069500029967030"
    ],
    [
      "-363217493650920574748",
      "440832554837922752423801025570"
    ],
    [
      "40125135492800341636",
      "2840885971773919997777362217250"
    ],
    [
      "166730363407080419566",
      "227918619974573869049649394560"
    ],
    [
      "299680196131537818691",
      "3018418682015030155631802534060"
    ],
    [
      "-137468744640802205132",
      "4802841523750242568921386068322"
    ],
    [
      "-1357785397315014314",
      "3482943148648559003802414906600"
    ],
    [
      "99778532263451016502",
      "1751499470735363195920708006680"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Andrej Dujella and Juan Carlos Peral’s prescribed-torsion rank table, z2z2old1011121314.html: https://dujella.github.io/tors/z2z2old1011121314.html\r\n\r\nTwelve supplied rational points checked exactly on the displayed model; the source lists them as independent. Rational torsion Z/2Z × Z/2Z.",
  "created_at": "2026-10-19 16:21:22",
  "updated_at": "2026-10-19 16:21:22"
}