curve #1922

y² + xy + y = x³ + x² − 10920091632464590365831264648975539x + 437651494057993449247068775775947593191303103178481

a-invariants: [1, 1, 1, -10920091632464590365831264648975539, 437651494057993449247068775775947593191303103178481]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/4ℤ
conductor (N): 515815207960723425334608728015834768460606
discriminant (Δ): 596247334661650554814754998954868668140031830794873130932902569912217678193691854407619124885574385664
Faltings height: 18.3841
naive height: 246.7413
primes of bad reduction: 2, 3, 11, 29, 41, 71, 83, 131, 191, 277, 317, 397, 461, 1069, 6143, 12577, 33586249
regulator: 46666441206.0781561426395154744613414676546852445063375296332
submitted by: dujella
submitted at: 2026-09-25 19:15:30 UTC
last updated: 2026-09-25 19:15:30 UTC

(12312962916337123, 17465954517603234702423470)
(67285511500842939, 2740790813470355147146630)
(45984212347729443, 5721494183071967029585390)
(63658075732213475, 681407101617676553902702)
(57081828073673891, 551746937417282363027054)
(46468625331642675, 5527304026709760117608782)
(113108473177593891, 25486327153555762916111854)
(-8906302459944157, 23112824697957639230384366)
(63489682889990683, 511303164918466268499686)
(-3704626064653973325/49, 9888282977010465021877712866/343)
(1685476156824117371/25, 350691194569447786722914054/125)

found by Elkies (2005)

last edited by dujella at 2026-09-25 19:15:30 UTC · history