curve #2111

y² + xy = x³ − 686314995056746592212563068699x + 185191943492922551492053276048924231453427409

a-invariants: [1, 0, 0, -686314995056746592212563068699, 185191943492922551492053276048924231453427409]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1286799043897115641009631514
discriminant (Δ): 5873624890364163987432438421136497529808901466977458924617355169939999334108751960527913984
Faltings height: 16.1386
naive height: 217.7170
primes of bad reduction: 2, 3, 7, 11, 13, 17, 29, 31, 41, 47, 53, 61, 113, 193, 281, 599, 613
regulator: 103884004.383278508761412488973949128598248526783244151
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:58:17 UTC
last updated: 2026-09-26 06:58:17 UTC

(22938451515193186/625, 197674823029467459720804109/15625)
(6840850634159794/25, 528578782590430901814737/125)
(5609575569486906262/19321, 8662528189915128516148025851/2685619)
(1642974854695977838/5329, 662618134790365107525703273/389017)
(-378900522424928, -19769672812209174913961)
(-81322809103214, -15507004396475680418183)
(372481499312909686, -227329599656153180979484223)
(-61853306622986926082/97969, -587312155001062629035100952007/30664297)

2-isogenous partner of curve#1109 (Dujella - Peral (2016)). Isogenous to curve#2110, curve#2112 (also ours).

last edited by Steps Unbounded at 2026-09-26 21:47:49 UTC · history