curve #4055

y² + xy + y = x³ − 21002225533046105932213261292638x + 35140343228020171366943571030989078985423672656

a-invariants: [1, 0, 1, -21002225533046105932213261292638, 35140343228020171366943571030989078985423672656]
c-invariants: [1008106825586213084746236542046601, -30361256549009429573199483750094191362760866244901]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 10749697643744007055089717979911548123312910 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 12
discriminant (Δ): 59439972322187309483206972238392985231333975195352293396898133618080565367443245026071681440000 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 12
Faltings height: 16.9392 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 12
naive height: 227.9801 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 12
primes of bad reduction: 2, 3, 5, 7, 23, 29, 43, 47, 53, 73, 79, 89, 113, 163, 227, 569, 587, 757, 2333, 6793, 11903
regulator: 42933171254.339936136123398938360310058427707909844303716471782
submitted by: dujella
submitted at: 2026-10-08 12:35:05 UTC
last updated: 2026-10-08 12:35:05 UTC

(-808929780620795, -227157063434187440731843)
(737980974464206, 141573360647817416786924)
(-1135333847510123, -239836307738777667645667)
(3498773623893685, 66994452932796733694477)
(1878611902002490, 48117323975737758792212)
(1401750928742917, 91949781375739571919293)
(2105959443467872, 15829573353101442197264)
(102455952419125, 181630437131000653749437)
(-289617189381320, -202974520949183686919488)
(5406565374325525, 282186948436095755380637)
(20800779364908475/4, 2063759414317351376714971/8)
(614339639695930117, 481504950430008888608324093)

induced by the rational Diophantine triple {723557861871/729372213346, -507212474925/729372213346, 12638391281568/9117152666825}

last edited by dujella at 2026-10-08 12:35:05 UTC · history