{
  "id": 2731,
  "curve_key": "3268976811929476367499689634646171707597773972161:-5877366022450814872908609428525272502858303595259807864431117467065911841",
  "ainvs": [
    "1",
    "0",
    "0",
    "-68103683581864090989576867388461910574953624420",
    "6802506970429183880681255237338026167411750400145087841636060266672400"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 335.1256844943265,
  "faltings_height": 25.767609773569433,
  "conductor": "4944555496787281270125087159390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "47",
    "71",
    "103",
    "131",
    "139",
    "223",
    "239",
    "271",
    "1669",
    "99312839"
  ],
  "discriminant": "225427872764028158027822043954604207698285139456368844840188670142237027714872895654341764709837516521231480517478382035564545021221705600000",
  "regulator": "15391455.55919110033359406684474687083565079395",
  "points": [
    [
      "245075709834578877903979679225/107584",
      "120561400968894713290183540866299017304659985/35287552"
    ],
    [
      "20473310573592798046803827036852632058/3189842436169",
      "92561080744653782349478699345030612309595839324667644264/5697100058949504197"
    ],
    [
      "102839472237203803196117557631087681183329993685901200900/528402951416503165496948590712689",
      "368403685868726986172249667520602770328327557954814190817893525580394841821477901840/12146407636925224163807205149831900881679557119863"
    ],
    [
      "5038493256669721878718449639554813596409752130/45632446952519585956561",
      "244469898845881262256421267529153447721897991352746938670742781498010/9747890373994798262911231869043559"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-019, rational kernel x=-70687215479339285336760. 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 20:19:47",
  "updated_at": "2026-09-26 20:19:47"
}