curve #1827

y² + xy = x³ − 160457317436491036800639760108090x − 369449120458315595021673906507946532059648303900

a-invariants: [1, 0, 0, -160457317436491036800639760108090, -369449120458315595021673906507946532059648303900]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 59581557002530875732300241072530 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 9
discriminant (Δ): 205433411615970021619276805826598115294740948127791947056612960285747003233559617713571171944960000 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 9
Faltings height: 17.5598 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 9
naive height: 234.0803 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 9
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 31, 107, 163, 563, 887, 1621, 1823, 6701, 9341
regulator: 397201531.62490499009241517970421655388907276201198024642
submitted by: dujella
submitted at: 2026-09-25 15:34:09 UTC
last updated: 2026-09-25 15:34:09 UTC

(-8450528037687760, -618898774000695657281350)
(-3593381099714128, -400918994155866467092678)
(-4813673043029260, -539814935920921995999850)
(-2652827186707420, -193770902631239314259290)
(-4626517877424970, -523335883699781103941590)
(59983109876191780, 14346548683378268587551910)
(-3961188083242030, -451660763783710695990940)
(16909838270812052, 1323815396421135305641526)
(24747665523582329837/16, 123108140081725236259934729483/64)

found by Klagsbrun (2020)

last edited by dujella at 2026-09-25 15:34:09 UTC · history