curve #2015

y² + xy + y = x³ + x² − 16343354562559064151871130832020659x − 42639589563151841387449703830240754991749490260239

a-invariants: [1, 1, 1, -16343354562559064151871130832020659, -42639589563151841387449703830240754991749490260239]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 515815207960723425334608728015834768460606
discriminant (Δ): 278599885277218173074913434406463374798232198523063441661134311025102299832552630915842633051060593659904
Faltings height: 18.7307
naive height: 247.9510
primes of bad reduction: 2, 3, 11, 29, 41, 71, 83, 131, 191, 277, 317, 397, 461, 1069, 6143, 12577, 33586249
regulator: 95572871590048.0637801257276916968273257567953807489792606887
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:01:04 UTC
last updated: 2026-09-26 05:01:04 UTC

(-80798915370981701/9, 274500997270689767965645018/27)
(336599987868429755, -180534803559351042642413178)
(-2840452675334806141/169, -33123153941941570010486991282/2197)
(69378569398313759979/25, -577266391702795324402060440202/125)
(-261845018561112986205/2209, -1571553710525034690568327542094/103823)
(-22214982573649715701/1225, -674893928715978429919383253638/42875)
(48686848720459834055/361, 98511324362790963311028781698/6859)
(-6917680745631079821/289, 89902555550208933544808843822/4913)
(42715876705635782899/9, -279078447722687877002308346302/27)
(-2554602346987114966309/30625, 145813605449385662186296633453986/5359375)
(401911069313213911179/1225, -7415278286317474854594436959478/42875)

2-isogenous partner of curve#1922 (Elkies (2005)).

last edited by Steps Unbounded at 2026-09-26 21:40:32 UTC · history