{
  "id": 2761,
  "curve_key": "16451970488306217134690764060935255611281:-2110201868313258406159769430161828980574122096817790337819321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-342749385173046190306057584602817825235",
    "2442363273510715747841541058367325989435284665192578072225"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 277.8037916499855,
  "faltings_height": 20.767504633123842,
  "conductor": "37185313994818665091723230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "29",
    "83",
    "181",
    "2099",
    "2733361",
    "6440141"
  ],
  "discriminant": "34171746473723442109680710636384737061680382132567423897311151405873137186047953448726281188570414583110041600000",
  "regulator": "3729197.352641103605736200146936132011872683790",
  "points": [
    [
      "21943666966226335359023928537489074711144265380990/2039392943780604606949287660241",
      "1114401657192325968475710505155899096250597110939777171105887795510821535/2912402321042539817372943120380299346313992039"
    ],
    [
      "54584142614285135053022030/5987809",
      "127249722279607641449760207776294816695/14652168623"
    ],
    [
      "783616939307584688431305442845144698344461470/73549359416310572290455961",
      "93270592876920580079188440531922713703537807031828520601737595435/630766096153050653801913902600105531459"
    ],
    [
      "15698463104715642008855568086035234630735598/1462776769056359744083009",
      "-369862139878987377120005300361202857916558107935100381148074983/1769159878565794507506804362510279777"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-005, rational kernel x=-85689871598856534129/4. Source: https://dujella.github.io/tors/z10.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 20:21:15",
  "updated_at": "2026-09-26 20:21:15"
}