curve #4383

y² = x³ − x² − 677306627965757529626257935159540433x + 119301667254399453475376497157678435925462248950082737

a-invariants: [0, -1, 0, -677306627965757529626257935159540433, 119301667254399453475376497157678435925462248950082737]
c-invariants: [32510718142356361422060380887657940800, -103076640507801127607660984690096000107237097766923840000]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 734375670289085539129194693801768623503331947200
discriminant (Δ): 13736866607123642983650570238897861445683593961485813915260222287850955952451747557275032044110892495104000000
Faltings height: 19.6397
naive height: 259.1239
primes of bad reduction: 2, 3, 5, 11, 17, 31, 37, 43, 47, 71, 89, 97, 137, 197, 433, 877, 1093, 1153, 2423, 50671, 363119
regulator: 523911721948.80802126602924787299055794444669389746648449082679
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:20:54 UTC
last updated: 2026-10-17 10:20:54 UTC

(741785317768845117, 158270517346575929637218800)
(24603165433946867, 320394558194378115648423300)
(97054055243574757, 233410608231037567671462000)
(1543294956830563021, 1658244528668402735446874592)
(37199916879382117, 306850770726003798367726800)
(-682083762054703043, 513760701631199439410809200)
(-397271295036188168, 570681182610850853329679925)
(6629179288719055792, 16939756409777875138416977025)
(739891228136688307, 152360658671742501478928100)
(-470070689599997723, 577766222523299563101123600)
(1150524633215664111, 928978546332014757133172728)
(-381362411804065859, 567570824721252750807694032)

BASE dujella/z2z2old1011121314.html#pre19 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:20:54 UTC · history