curve #4258

y² + xy + y = x³ − x² − 4413691444170835397x + 3568990755862312193467697725

a-invariants: [1, -1, 1, -4413691444170835397, 3568990755862312193467697725]
c-invariants: [211857189320200099041, -3083608012111680383215190388945]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 8856428161875443650508960054718
discriminant (Δ): 143024478860474788439003078567235623087520891072479232
Faltings height: 9.3361
naive height: 140.4073
primes of bad reduction: 2, 3, 7, 11, 23, 29, 37, 103, 107, 257, 353, 2377, 54121, 2013001
regulator: 12310347919.5763849141585400219534465770847214665790521738219
submitted by: The Wren
submitted at: 2026-10-15 20:39:44 UTC
last updated: 2026-10-15 20:39:44 UTC

Witness: 11 independent points log in to add more points →

(-2211393737, 50151928568864)
(794265535, 23757050533184)
(1206851401, 296744571476)
(4870000079/4, 1364077130083/8)
(1249862831, 2227370128336)
(-52032054809/25, 7644126975253696/125)
(16193325799/25, 3916787478284608/125)
(41939162951/25, 3720166519954784/125)
(736476982447/529, 134737420542902464/12167)
(1133903545999/625, 611767303744365632/15625)
(4770036494167/169, 10389855556302387008/2197)

Commentary

Found by specializing the family associated with curve#802 at T = -65/3. The original PARI/GP computation returned rank bounds [11,11]. Eleven rational points are supplied.

last edited by The Wren at 2026-10-15 20:39:44 UTC · history