curve #4621

y² + xy + y = x³ + x² − 101772327397613879567642062451364835745x + 395159959510136823176380977908067959221359063055636173407

a-invariants: [1, 1, 1, -101772327397613879567642062451364835745, 395159959510136823176380977908067959221359063055636173407]
c-invariants: [4885071715085466219246818997665512115761, -341418205016758215261031202775711713411605372962560994692009]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 12282023191585328240966136440298451368031941176317794532149510
discriminant (Δ): 6132837481363973595281503078729932569908196062154980728607860248864589936247524002827215302492307456000000000000
Faltings height: 20.5183
naive height: 274.1610
primes of bad reduction: 2, 3, 5, 7, 11, 37, 53, 97, 151, 163, 179, 229, 257, 269, 313, 379, 433, 449, 577, 821, 3529, 4409, 6257, 11489, 32793913
regulator: 186724931077532897.571620530845394442689695367803796253134987909838380272
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:30:39 UTC
last updated: 2026-10-19 03:30:39 UTC

(-2522406699128420513, 25215516208833799118625473696)
(5699819545402000797, 501468117108747131030283976)
(5893117032150232047, 254506195242903287265408976)
(6508721221016382377, 2912756604547361821345126256)
(7021441193811082047, 5170402988366497733098458976)
(15005436674811082047, 47399291455975513975090458976)
(21125669448520906047, 87597996678955038741220890976)
(22115197231937386047, 94660385696975142889793082976)
(365674001827438582047, 6990006014636333011456307958976)
(501872893514586416447, 11240963334279117298004244865376)
(-18868305304462208751257/7569, 16572454179276595751194586241082928/658503)
(52778491871495578423/9, 2676898808707047812759512352/27)
(58304932455955450423/9, 75080448131611025211568408352/27)
(256573336321363852057/81, 7454738953606416645736461043504/729)
(5343530499279407001527/841, 54679357253775237346300625965664/24389)
(5547702852473163447167/961, 5022095810214516637134816954016/29791)
(8020658359168539272343/1369, 2618496890108467955769515211328/50653)

X400, T=-1259/5670

last edited by Andrii Prokhorenkov at 2026-10-19 03:30:39 UTC · history