curve #6352

y² = x³ + x² − 6570275283780692877972820625x + 204324488171532213512172412018604014924959

a-invariants: [0, 1, 0, -6570275283780692877972820625, 204324488171532213512172412018604014924959]
c-invariants: [315373213621473258142695390016, -176536357780205724713798692823622725067504640]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 428449346499782847865546723741853713508947907315223370001767453067391648
discriminant (Δ): 116908232639140604942067121758527132832223867418567483360574831693134079476744466432
Faltings height: 14.7990
naive height: 203.7707
primes of bad reduction: 2, 3, 11, 13, 504752329, 17606028301, 27071274101, 7713107588612693947, 16819551137422139107
regulator: 366632600921051387106.27055151228080637678285685004384119074176577169100801150541
submitted by: apkorte
submitted at: 2026-11-01 05:37:24 UTC
last updated: 2026-11-01 05:37:24 UTC

(60215958204355, -164407480977773976228)
(44593303606363, 3284671815503734500)
(33343669974139, 149395115924234426532)
(-34604385481823, 624697797696217354164)
(-6877878393989/25, 56752209418059203589684/125)
(1569507429738355, 62097857949751267283772)
(63182652009859, -203531865452177960412)
(197495746382461/4, 135577055414799333621/8)
(48973832883082, -3680125036529658849)
(50312111938899, -33399770204472900228)
(-63450305444573, 604783646496315736164)
(-74557360746773, -528902082331754752764)
(27133755991867, 214534886937122481444)
(-93542143656437, 20395053820970803260)
(44548904350189, -6155966102798315232)
(98333690062561, 713501315101896851244)
(196509765194269/4, 85050221171255227173/8)
(578259637289251/25, 31801774982314051443924/125)
(44596564698925, -2969659437410766672)
(93274514798275, 634811885624478734172)
(55164385418563, 98744878094697691740)

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