curve #3892

y² + xy + y = x³ − x² − 49186267083307075639436170362x + 4297160714245579319048638636001986527832761

a-invariants: [1, -1, 1, -49186267083307075639436170362, 4297160714245579319048638636001986527832761]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 967642646854693114215369268426236209018710865441870812919210
discriminant (Δ): -361404504705799377658787756170113733609995318194314730829758324018531607088563200000000
Faltings height: 15.3901
naive height: 209.8562
primes of bad reduction: 2, 5, 7, 13, 29, 41, 53, 1951, 9199, 522927263, 1797946279693876871312345160003338789
regulator: 561869543887156617.3943739169227164016056310673109653720450766845330694122964
submitted by: 7fff-zip
submitted at: 2026-10-04 14:09:09 UTC
last updated: 2026-10-04 14:09:09 UTC

(-255232750531269, -473589025118420138491)
(-210348794741519, -2310023808537516077241)
(-193352895189055, -2564937276814878493273)
(-85689233569359, 2807616227756244022919)
(-13772044594455, 2229785656920910065687)
(-2538421914119, -2102855166340798284041)
(49427731788561, 1409521887782990220039)
(67529826858481, 1132949817440180418759)
(81523747394481, -910565042592035165241)
(89874988558481, 776216395521430822759)
(90182060507889, 771281243276303903559)
(100757181334481, -603472463818435525241)
(125109890390481, -318987323395621701241)
(125369490606941, 318118757946133062719)
(155880483503221, -646280700022768335621)
(187858382849081, -1298759301889427637641)
(188656724156481, 1316202776612059476759)
(244641726320481, 2627898389707193288759)
(349414103674545, -5456265254936968301113)

X1020, t=33/29

last edited by 7fff-zip at 2026-10-04 14:09:09 UTC · history