curve #1105

y² + xy = x³ − 4422329901784763147754792226039053294186858800x + 98943710602886706347390586357680210847183616798063680624530387016000

a-invariants: [1, 0, 0, -4422329901784763147754792226039053294186858800, 98943710602886706347390586357680210847183616798063680624530387016000]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/12ℤ
conductor (N): 358210529915244759591648810 ☆ record for ℤ/12ℤ torsion, rank ≥ 4
discriminant (Δ): 1305982276183610316096820005065297173531409098221829414851668354853561611521102986032953668531973483814864823544424056100825238319828824000 ☆ record for ℤ/12ℤ torsion, rank ≥ 4
Faltings height: 25.2290 ☆ record for ℤ/12ℤ torsion, rank ≥ 4
naive height: 326.9226 ☆ record for ℤ/12ℤ torsion, rank ≥ 4
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 29, 139, 593, 859, 11503, 1563539
regulator: 160114183.4355027631154077670150369410011989284
submitted by: dujella
submitted at: 2026-09-23 19:55:12 UTC
last updated: 2026-09-23 19:55:12 UTC

(34041292371237064006426894957396/630763225, 66204769563702181648309208636101377723512158736/15841618395875)
(-3925299848487219649803111424581267172504307567199407913441245040118981868/137194342227669518519498512006351993035192663119881, 22842024253754429037657080561785875269591709783412591343934007046468346667249098446804083045186137431599118192/1606957173720562553134392492036223587414467589358506324505368702826998453221)
(34396396322282805835691520585756626787219271296794743776416028880395727371083219104/484900109842890380829228824741997715427442294522315097791225, 4026147990177777010257053688570100097820122036459101202734213304650511740019205983949300520214472637860883761166365597379528/337659072927765759013309287184879322340988288683024746195867377940161451743713659393482125)
(-1360157677325654026821400382914648821099795934113255313220731687021750378269683124822984403863493256698970/95210567235402459537983154136285200689965053149892391652528137442637637800647451769, 370685526171259919765184269719379305784467970007299015848801757929842196923020385238912398229715366382305152064525129755759650894029117089726075578691605210700/29378372210259503406799373066960078670967941610317399339241376984463056059070657785847424233217595325991594921693465686427853)

found by Fisher (2008)

last edited by dujella at 2026-09-23 19:55:12 UTC · history