{
  "id": 3120,
  "curve_key": "3134782446974193495860512162662449104651783963333174401:-5854944959477268826394676502953678119526320579782472256947247574540827129981521601",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-65307967645295697830427336722134356346912165902774467",
    "6776556666061653734253097820671526771886795499021732626074384890594739542801859"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 376.55335825784306,
  "faltings_height": 29.320158974308406,
  "conductor": "2603348955675569045873307484526694064917261974747900874693810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "37",
    "67",
    "71",
    "83",
    "97",
    "127",
    "149",
    "191",
    "193",
    "683",
    "947",
    "1481",
    "1951",
    "3457",
    "14008947836626425239"
  ],
  "discriminant": "-2011174270050636328301112822431930831743045343284277992236255883348383349218526221894927781102384865693501720077763078300447429091225685218518855424000000000000",
  "regulator": "2592486636509.80077522205220039024725851696751875887882930881",
  "points": [
    [
      "1788826751214181251515755973484767667/1556381401",
      "2338082497983241577784513418441718023396199558840014966/61400802650851"
    ],
    [
      "-5312300021776083430523368917/49",
      "-1216688688027523408611134039453543851548962/343"
    ],
    [
      "-12863776709018956287677733",
      "-2759444712834869445029809501793336961134"
    ],
    [
      "316843215496912418503345964732967/39601",
      "-5636997539277726057243000021433979315805033489266/7880599"
    ],
    [
      "832441435507833836100408800572093/1159929",
      "-22677708471845722766044238616688291506982031415172/1249243533"
    ],
    [
      "282432251269388148216746667",
      "-3295531753207275854427540794423250665534"
    ],
    [
      "40998841858375946773770894667/81",
      "-7412765162229735171573623893194825156052286/729"
    ],
    [
      "-144287436906116137982890983",
      "-3632598978213189037122671847288931741634"
    ],
    [
      "-5020971851185755453273846459702611493/63504504001",
      "-54141603227670898719906951183559579721012222970463799534/16003198512756001"
    ],
    [
      "-549754073815107967161679644699/100489",
      "-85081388450298598768448014709957725683914804314/31855013"
    ],
    [
      "4748212234396034210903864020777/19881",
      "-6142853430788805467802701483910296551162143914/2803221"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z2old1011121314-046, rational kernel x=2374994013564696008458221867/4. Source: https://dujella.github.io/tors/z2z2old1011121314.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:38:13",
  "updated_at": "2026-09-26 20:38:13"
}