curve #4612

y² + xy + y = x³ − x² − 9587363242690973783330492x + 10536060714562308983254191000903086975

a-invariants: [1, -1, 1, -9587363242690973783330492, 10536060714562308983254191000903086975]
c-invariants: [460193435649166741599863601, -9103156457379764091071199774443067760425]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ
conductor (N): 27184304298374298547706309213830981063446
discriminant (Δ): 8444089760264762102204390799333154956340588931961752986189218536121006292992
Faltings height: 13.3098
naive height: 184.1811
primes of bad reduction: 2, 3, 7, 17, 41, 43, 67, 103, 167, 173, 271, 379, 563, 1009, 1663, 2441, 2731, 55819
regulator: 894117433004.043116447416965885231383462375768144813970777709199962
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:23:37 UTC
last updated: 2026-10-19 03:23:37 UTC

(-683285201675, 4094869430802129349)
(-574906560395, 3982195916754169029)
(426471878421, 2554385401319674117)
(900913764213, 1621694930592768709)
(1241082198903, 740927975682744709)
(1361753764533, 75049767031660357)
(2905706152497, 2685375623252222305)
(2919835239931, 2726793997678006087)
(3064804363125, 3152847088122686149)
(5760191578527, 12100949837981621707)
(-40040707379427/169, 7858466461467297878665/2197)
(22111553593117/9, 36335563635728961479/27)
(29628066057069/25, 114453982378966501937/125)
(5058401396914849/4225, 241562468454210242034513/274625)

X660, T=75/41.

last edited by Andrii Prokhorenkov at 2026-10-19 03:23:37 UTC · history