curve #6207

y² + xy = x³ − x² − 3469793642325789x + 77364990770745149899289

a-invariants: [1, -1, 0, -3469793642325789, 77364990770745149899289]
c-invariants: [166550094831637881, -66843351276448382770615245]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 542582922844832461335825536708869747629322206
discriminant (Δ): 87898433500862858736403736946836899115950197372
Faltings height: 7.8011
naive height: 118.9622
primes of bad reduction: 2, 3, 54240902959, 555733663511960403969237748737913
regulator: 35332345242690.87130823657811788333110797582056484608065831812226522246
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-30 17:19:44 UTC
last updated: 2026-10-30 17:19:44 UTC

(-142044472641251/2621161, 1383401415990709647332/4243659659)
(-226010381/4, -2439844204315/8)
(-32746190, 394824361777)
(-66047326465760/1181569, 399350626079478877531/1284365503)
(1015716562166770/2927521, 31930790337512780093983/5008988431)
(192582241912/6889, 26891524055436425/571787)
(1939243193/64, -3550814022649/512)
(197497552, -2663843692997)
(25413395, 74812137537)
(26526340, -63173664743)
(30227512, 10020515515)
(30352552, -3334619555)
(32222059873051/1062961, 6803838173660145839/1095912791)
(3759808096/25, -214961640850159/125)
(418784146, 8489237069089)
(746000356/25, -2491331400361/125)

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