{
  "id": 2118,
  "curve_key": "3200107265570126925334561:-5724621848523524409337464734973797809",
  "ainvs": [
    "1",
    "0",
    "0",
    "-66668901366044310944470",
    "6625719732081856769026747158085412"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    10
  ],
  "naive_height": 169.27567968477493,
  "faltings_height": 11.4332966180618,
  "conductor": "402308013184770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "109",
    "113",
    "439",
    "1039"
  ],
  "discriminant": "103763899636216227951855841840106378044897513012976025600000",
  "regulator": "6326.1727367454751660647127968232614536914211",
  "points": [
    [
      "1333169210776/9",
      "17021116337099386/27"
    ],
    [
      "10823612723760190012/72607441",
      "1358527016659317157133578/618688004761"
    ],
    [
      "74320239360073850956822499762456/498555536367209700625",
      "18188087035130131166572528916721253529977054/11131926112508536972040305765625"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Rank >= 3 with torsion Z/10 from the universal X_1(10) family at s=4/113 (t=s^2(2s-1)/(s-1)^2); conductor 402308013184770.",
  "created_at": "2026-09-26 08:51:52",
  "updated_at": "2026-09-26 08:51:52"
}