curve #2032

y² + xy = x³ − 23799921494493543155993219000205x + 44542952883353601217905491124577269137295688977

a-invariants: [1, 0, 0, -23799921494493543155993219000205, 44542952883353601217905491124577269137295688977]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/6ℤ
conductor (N): 2133955072923930972049654590270 ☆ record for ℤ/6ℤ torsion, rank ≥ 9
discriminant (Δ): 5672620567959354026775482125612755163892229680299426366205344568676168169296418511625000000000
Faltings height: 16.8485
naive height: 228.3553
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 37, 41, 43, 47, 127, 719, 4733, 7253, 18911
regulator: 31739763721.212457396064270778909219221865955855657251530
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:04:15 UTC
last updated: 2026-09-26 05:04:15 UTC

(144434610580200432/49, -143263900088919473039247/343)
(6748538572870944, 437350455722285136351753)
(20784604597693391746/9, 94757082816393758386421220181/27)
(412313481099574579176/139129, -321636874053489705528721125699/51895117)
(11051690738711216514/3481, -6440164836941535368122738563/205379)
(867090820697300035464/292681, 949922018274790095691143351363/158340421)
(133046407026208155174/44521, 97292694381397804258727445393/9393931)
(7085652823868827015150674/1498541521, 11266857710847793079338752673575504393/58010040819431)
(7873203994095287019426/1885129, 347190251650156675769910362709051/2588282117)

2-isogenous partner of curve#1216 (Klagsbrun (2020)).

last edited by Steps Unbounded at 2026-09-26 21:44:31 UTC · history