curve #2118

y² + xy = x³ − 66668901366044310944470x + 6625719732081856769026747158085412

a-invariants: [1, 0, 0, -66668901366044310944470, 6625719732081856769026747158085412]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/10ℤ
conductor (N): 402308013184770
discriminant (Δ): 103763899636216227951855841840106378044897513012976025600000
Faltings height: 11.4333
naive height: 169.2757
primes of bad reduction: 2, 3, 5, 7, 11, 31, 109, 113, 439, 1039
regulator: 6326.1727367454751660647127968232614536914211
submitted by: Steps Unbounded
submitted at: 2026-09-26 08:51:52 UTC
last updated: 2026-09-26 08:51:52 UTC

(1333169210776/9, 17021116337099386/27)
(10823612723760190012/72607441, 1358527016659317157133578/618688004761)
(74320239360073850956822499762456/498555536367209700625, 18188087035130131166572528916721253529977054/11131926112508536972040305765625)

Rank >= 3 with torsion Z/10 from the universal X_1(10) family at s=4/113 (t=s^2(2s-1)/(s-1)^2); conductor 402308013184770.

last edited by Steps Unbounded at 2026-09-26 08:54:12 UTC · history